You can't just make something out of something that is not. You know the resolution of the projector is 800x600? It may SUPPORT HD...but is it?
My dad has a Yamaha RX-V663 receiver, which accepts HDMI input and output. He wants to use it with a projector, an Epson Powerlite S5, which unfortunately only has analog inputs, so it won't show any digital sources the receiver chucks at it, and the analog signals we use (usually composite) look awful. I want him to have the whole HD experience with his Chromecast and Blu-ray, so I've been looking into how to convert the receiver's HDMI signal to VGA. Audio isn't necessary, since the receiver is taking care of it.
I've seen some cables that purport to convert HDMI to VGA in-line, but I find them a little bit suspect, since there's complex conversion that needs to be done to the HDMI's digital signal to convert it to analog. They look like they're more designed for computers than receivers, which probably would do the conversion by itself.
Others have suggested I need a converter box, of which I have found several examples ranging in price from $5 to $100. This one seems the most appealing, since it's compact and claims to draw its power from the HDMI port, but I can't find any reviews about it, so this could just be a bit of a snow job.
I'd also have to run the signal through a splitter, since the receiver has only one output, which I have a feeling would screw something up. What should I do?

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic