Similar to this question (that one doesn't want to use Flash, though, while I'd be fine with it):
Is there a reliable, works-in-most-browsers way to have a full-area Video background in an HTML page, the Video starting to play automatically and looping endlessly, and being able to put HTML on top of it?
I'm fine with using a Flash video player.
"Most browsers" means, support for IE 6 would be perfect, but if it can't be done it can't be done. IE7 is a must, though, as are all the modern browsers Firefox 2.x and 3.x, and the Webkit family. Don't hesitate to also post solutions that have a more limited scope, though.
Ideally, it would automatically stretch to 100% document width anmd resize the video accordingly.
I'm open about which video format to use, although H.264 would be perfect as I can produce that quickly.
Also ideally, this could be done with a minimalistic player component that works out of the box (i.e. doesn't require me having Flash to compile a movie). A simple volume control / mute button would be nice but is not mandatory.
Unlike in the question I linked to, waiting for HTML 5 is not an option.