Hardware/software to project video wirelessly?
Wi-Fi enabled projectors have been around for several years, at least.

A cursory Google search for "wifi enabled projector" turns up that and several other articles, plus reviews and some product listings. The primary complaint seems to be bandwidth; however I did not find any reviews including more recent Wi-Fi standards like 802.11g/n.

That said, it was a cursory search. I saw lots of other results that I didn't have time to click on. Some of them looked a lot more current, and I did find something that looks like a present-day product listing of wireless projectors.

My advice would be to shop around, read reviews, and get a good return/exchange policy if you decide to buy one (so you can test it with relatively low risk).