I've heard that they have a patent cross license agreement, which is why AMD can use x86 and Intel can use AMD64, but I hadn't heard about the ownership.

I don't see Intel listed at http://www.nasdaq.com/symbol/amd/institutional-holdings

Where do you see they have an ownership stake? How much is it?

It was IBM who forced Intel and AMD to sign the agreement. From CNET:

"Early 1980s--IBM chooses Intel's so-called x86 chip architecture and the DOS software operating system built by Microsoft. To avoid overdependence on Intel as its sole source of chips, IBM demands that Intel finds it a second supplier.

1982--Intel and AMD sign a technology exchange agreement making AMD a second supplier. The deal gives AMD access to Intel's so-called second-generation "286" chip technology."

I don't think so. They certainly don't show up on any of required disclosures of major AMD holders, so if they do hold AMD stock it is less than 1%.

You do not recall correctly.

actually I do, but it turns out it was not 'sizeable' and it was a long time ago, so it may have been divested by now.