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, 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 in Reno, just 200 miles away, to collect and invest the company’s profits, Apple sidesteps state income taxes on some of those gains.California’s corporate tax rate is 8.84 percent. Nevada’s? Zero.