Now that Apple Inc. (NASDAQ:AAPL), the most valuable technology company, faces a lawsuit and proxy fight by a dedicated investor and hedge fund manager known for value investing, the company is a technology player in a very unusual position: It’s doing very well.

Last year, hedge funds such as Daniel Loeb’s Third Point Capital and Jeffrey Smith’s Starboard Value mounted challenges against foundering companies.

Loeb went after Yahoo Inc. (NASDAQ:YHOO), the No. 3 search engine, and got himself and three colleagues elected as directors, forced out a CEO and then proceeded to have the new CEO, Marissa Mayer, take steps to sell offshore assets in China and Japan that brought new cash to the Sunnyvale, Calif., company.

For the past year, the return on Yahoo shares has exceeded 27 percent. They were at $21.17 in Thursday trading.

Smith’s challenge to take over New York-based AOL (NYSE:AOL), the No. 7 website, failed but had the effect of forcing CEO Timothy Smith to move the company more aggressively to recover momentum. Over the past year, AOL shares have more than doubled, to $31.38.

By contrast, after setting an all-time high of $705.07 last September, the same day as the iPhone 5 shipped, the return on Apple shares has been negative 1 percent, including the dividend reinstated after investors fretted about the Cupertino, Calif., company’s pile of cash and investments, which reached a staggering $137.1 billion by Dec. 31.

Einhorn, who has previously sounded warnings that Lehman Brothers would collapse in 2007 and then said shares of Green Mountain Coffee Roasters Inc. (NASDAQ:GMCR) were overpriced last year, said he had approached Apple CFO Peter Oppenheimer about dealing with the cash last year. He last spoke with officials of the Cupertino, Calif., company on Wednesday.

The company, though, has refused Einhorn’s request to drop a resolution for its Feb. 27 annual meeting that would change the company’s capital structure to bar it from issuing preferred shares and other instruments that might become ways to pass along cash.

But after his challenge, the company issued a statement that it would continue to "enhance corporate governance and serve our shareholders' best interests" and consider methods of dealing with the cash. Apple disputed the Greenlight claim that the rule changes would preclude issuing preferred stock.

So now, Einhorn has asked all Apple shareholders to join him as a means to deal with the question. Greenlight owns 1.3 million shares, valued around $550 million.

More than 25 percent of Apple shares is owned by 10 major investors, mainly mutual fund complexes Fidelity Management, Vanguard Group and State Street Global Advisers (NYSE:STT), as well as the TIAA-CREF, the asset manager for the nation’s teachers and college professors.

Faced with a negative return on Apple shares and dealing with Einhorn’s claim that each share carries $145 in cash might win him support at the annual meeting.

Other technology companies that accumulated so much cash have paid special dividends. The best example is Microsoft Corp. (NASDAQ:MSFT), the No. 1 software company, which paid one in 2004, when it had $56 billion. Shareholders received an immediate $3 per-share, and the Redmond, Wash., company bought back $30 billion worth of shares as part of a four-year, $75 billion campaign.

Buoyed by success from the iPad and iPhone product lines, as well as other items and services, Apple has reported record gains in revenue and income for the past two years. While it reinstated its dividend in 2012, its cash and investments grew from $98.1 billion last Dec. 31 to $117.2 billion on June 30 and finally to $137.1 billion by Dec. 31.

The company usually has a quiet annual meeting, where management, under Chairman Arthur Levinson, the former CEO of Genentech Inc., gets its resolutions passed, including defeating ones from religious organizations seeking a human rights committee to remediate labor conditions in the Chinese plants of its contract manufacturers.

Apple could change its mind. Or, since the directors, including Cook, Levinson and former U.S. Vice President Al Gore, are expected to be present, Apple could make a major announcement at the meeting.

The Einhorn challenge didn’t do much for Apple’s share price, which was $468.25, up $13.55 at the close.