What exactly does David Einhorn want from Apple?

Einhorn at the World Series of Poker. He finished 18th.

FORTUNE — David Einhorn, the 44-year-old founder of Greenlight Capital and the author of
Fooling Some of the People All of the Time
, is a complicated guy.

He’s a billionaire hedge fund manager who made a killing shorting Lehman Bros. and Allied Capital, finished 18th in the World Series of Poker, almost bought a piece of the Mets, tried to force Microsoft (AAPL) to fire Steve Ballmer, paid the second largest individual fine in U.K. history for alleged insider trading and has donated heavily to charitable causes — including the Michael J. Fox Foundation and the Democratic Party.

He also owns, through Greenlight, a big stake in Apple (AAPL) — 1.09 million shares as of September, down from 1.45 million three months earlier. And like many major Apple investors who have watched the value of their holdings drop 35% in the past four months, he looks at the company’s $137 billion in cash and marketable securities and feels it burning a hole in his pocket. On Thursday, he issued an open letter to Apple shareholders.

“Greenlight believes Apple is a phenomenal company filled with talented people creating iconic products that consumers around the world love,” it begins. “However, like many other shareholders, Greenlight is dissatisfied with Apple’s capital allocation strategy.”

“We believe,” the letter quotes Einhorn as saying, “Apple must examine all of its options to unlock the growing value of its balance sheet for all shareholders.”

What does he propose? He wants Apple to create a perpetual preferred stock — a kind of extra special dividend — that would be distributed at no cost to Apple’s existing shareholders, like him.

According to the letter, Einhorn first floated the idea last May, and over the summer had “ongoing discussions” with Apple management about it.

But Apple guards its cash pretty closely, and apparently it doesn’t like to be told what to do with it — even by investors that own more shares than Tim Cook.

From Apple’s Proxy: See item ii.

In September, the company rejected Einhorn’s preferred shares plan, and in January it went even further: It included in its proxy statement a four-part proposal to amend the company’s articles of incorporation to, among other things, “eliminate ‘blank check’ preferred stock.”

Apple didn’t say why it felt the sudden need to rewrite its bylaws, but its response has clearly put Einhorn’s nose out of joint. Not only has he started a proxy fight — urging shareholders to vote against the amendment — but he’s sued Apple to break it into four parts as, he believes, SEC rules require, making it easier to knock the parts down one at a time.

It’s a complicated fight. But then Einhorn is a complicated guy.

UPDATE: There have been, as they say, further developments. See:

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