RENO, Nev. >> Apple, the world’s most profitable technology company, doesn’t design iPhones here. It doesn’t run AppleCare customer service from this city. And it doesn’t manufacture MacBooks or iPads anywhere nearby.

Yet, with a handful of employees in a small office here in Reno in a company subsidiary named Braeburn Capital, Apple has done something central to its corporate strategy: It has avoided millions of dollars in taxes in California and 20 other states.

Apple’s headquarters are in Cupertino, Calif. By putting an office to collect and invest the company’s profits out of Reno, just 200 miles away, Apple sidesteps state income taxes on some of those gains.

California’s corporate tax rate is 8.84 percent. Nevada’s? Zero.

Setting up an office in Reno is just one of many legal methods Apple uses to reduce its worldwide tax bill by billions of dollars each year.

As it has in Nevada, Apple has created subsidiaries in low-tax countries like Ireland, the Netherlands, Luxembourg and the British Virgin Islands — some little more than a letterbox in Luxembourg or an anonymous office here — that help cut the taxes it pays around the world.

Almost every major corporation tries to minimize its taxes, of course. For Apple, the savings are especially alluring because the company’s profits are so high. Wall Street analysts predict Apple could earn up to $45.6 billion in its current fiscal year — which would be a record for any U.S. business.

Braeburn is a variety of apple that is simultaneously sweet and tart. When someone in the United States buys an iPhone, iPad or other Apple product, a portion of the profits from that sale is often deposited into accounts controlled by Braeburn, and then invested in stocks, bonds or other financial instruments, say company executives. Some profits from those investments are shielded from California tax authorities by virtue of Braeburn’s Nevada address.

Since founding Braeburn in 2006, Apple has earned more than $2.5 billion in interest and dividend income on its cash reserves and investments around the globe. What’s more, Braeburn allows Apple to lower its taxes in other states because many of those jurisdictions use formulas that reduce what is owed when a company’s financial management occurs elsewhere.

While Apple’s Reno office helps the company avoid state taxes, its international subsidiaries — particularly the company’s assignment of sales and patent royalties to other nations — help reduce taxes owed to the U.S. and other governments.

The Luxembourg subsidiary, named iTunes S.ar.l., has just a few dozen employees, according to corporate documents filed in that nation and a current executive. But when customers across Europe, Africa or the Middle East — and potentially elsewhere — download a song, television show or app, the sale is recorded in this small country, according to current and former executives.

The country has promised to tax the payments collected by Apple and numerous other tech corporations at low rates if they route transactions through Luxembourg. Taxes that would have otherwise gone to the governments of Britain, France, the United States and dozens of other nations go to Luxembourg instead, at discounted rates.

In 2011, iTunes S.ar.l.’s revenue exceeded $1 billion, according to an Apple executive, representing roughly 20 percent of iTunes’ worldwide sales.

Apple serves as a window on how technology giants have taken advantage of tax codes written for an industrial age and ill-suited to today’s digital economy. Some profits at companies like Apple, Google, Amazon, Hewlett-Packard and Microsoft derive not from physical goods but royalties on intellectual property, like the patents on software that makes devices work.

Other times, the products themselves are digital, like downloaded songs. It is much easier for businesses with royalties and digital products to move profits to low-tax countries than it is, say, for grocery stores or automakers. A downloaded application, unlike a car, can be sold from anywhere.

The growing digital economy presents a conundrum for lawmakers overseeing corporate taxation: Though technology is now one of the nation’s largest and most valued industries, many tech companies are among the least taxed, according to government and corporate data.

Even among tech companies, Apple’s rates are low. And while the company has remade industries, ignited economic growth and delighted customers, it has also devised corporate strategies that take advantage of gaps in the tax code, according to former executives who helped create them.

Apple, say former executives, has been particularly talented at identifying legal tax loopholes and hiring accountants who are known for their innovation. In the 1980s, for instance, Apple was among the first major corporations to designate overseas distributors as “commissionaires,” rather than retailers, said Michael Rashkin, Apple’s first director of tax policy, who helped set up the system before leaving in 1999. Because commissionaires never technically take possession of inventory — which would require them to recognize taxes — the structure allowed a salesman in high-tax Germany, for example, to sell computers on behalf of a subsidiary in low-tax Singapore.

In addition, Apple was a pioneer of an accounting technique known as the “Double Irish with a Dutch Sandwich,” which reduced taxes by routing profits through two Irish subsidiaries — today named Apple Operations International and Apple Sales International — and the Netherlands and then to the Caribbean. In 2004, Ireland, a nation of less than 5 million, was home to more than one-third of Apple’s worldwide revenues, according to company filings.

Without such tactics, Apple’s federal tax bill in the United States most likely would have been $2.4 billion higher last year, according to a recent study by a former Treasury Department economist, Martin A. Sullivan. As it stands, the company paid cash taxes of $3.3 billion around the world on its reported profits of $34.2 billion last year, a tax rate of 9.8 percent. (Apple does not disclose what portion of those payments were in the United States, or what portion are assigned to previous or future years.)

By comparison, Wal-Mart last year paid worldwide cash taxes of $5.9 billion on its booked profits of $24.4 billion, a tax rate of 24 percent, which is about average for non-tech companies.

Apple’s domestic tax bill has piqued particular curiosity among corporate tax experts because though the company is based in the United States, its profits — on paper, at least — are largely foreign. While Apple contracts out much of the manufacturing and assembly of its products to other companies overseas, the majority of Apple’s executives, product designers, marketers, employees, research and development and retail stores are in the United States. Tax experts say it is therefore reasonable to expect that most of Apple’s profits would be American as well. The nation’s tax code is based on the concept that a company “earns” income where value is created, rather than where products are sold.

However, Apple’s accountants have found legal ways to allocate about 70 percent of its profits overseas, where tax rates are often much lower, according to corporate filings.

Neither the government nor corporations make tax returns public, and a company’s taxable income often differs from the profits disclosed in annual reports. Companies report their cash outlays for income taxes in their annual Form 10-K, but it is impossible from those numbers to determine precisely how much, in total, corporations pay to governments. In Apple’s last annual disclosure, the company listed its worldwide taxes — which includes cash taxes paid as well as deferred taxes and other charges — at $8.3 billion, an effective tax rate of almost a quarter of profits.

However, tax analysts and scholars said that figure most likely overstated how much the company would hand to governments because it included sums that might never be paid. “The information on 10-Ks is fiction for most companies,” said Kimberly Clausing, an economist at Reed College who specializes in multinational taxation. “But for tech companies it goes from fiction to farcical.”

Apple, in a statement, said it “has conducted all of its business with the highest of ethical standards, complying with applicable laws and accounting rules. We are incredibly proud of all of Apple’s contributions.”

The statement also said that Apple “pays an enormous amount of taxes which help our local, state and federal governments. In the first half of fiscal year 2012, our U.S. operations have generated almost $5 billion in federal and state income taxes, including income taxes withheld on employee stock gains, making us among the top payers of U.S. income tax.”

The statement did not specify how it arrived at $5 billion, nor did it address the issue of deferred taxes, which the company may pay in future years or decide to defer indefinitely. But the $5 billion figure appears to include taxes ultimately owed by Apple employees.

The sums paid by Apple and other tech corporations is a point of contention in the company’s backyard.

A mile and a half from Apple’s Cupertino headquarters is De Anza College, a community college that Steve Wozniak, one of Apple’s founders, attended from 1969 to 1974. Because of California’s state budget crisis, De Anza has cut more than a thousand courses and 8 percent of its faculty since 2008.

Now, De Anza faces a budget gap so large that it is confronting a “death spiral,” the school’s president, Brian Murphy, wrote to the faculty in January. Apple, of course, is not responsible for the state’s financial shortfall, which has numerous causes. But the company’s tax policies are seen by officials like Murphy as symptomatic of why the crisis exists.

“I just don’t understand it,” he said in an interview. “I’ll bet every person at Apple has a connection to De Anza. Their kids swim in our pool. Their cousins take classes here. They drive past it every day, for Pete’s sake.

“But then they do everything they can to pay as few taxes as possible.”

© 2012 The New York Times Company