Tried the .xap file download method from Windows Store as I have an 820 (ext sd card). Thought I'd cracked it only to realise that once you download it, it still wants to INSTALL on the internal storage, NOT the sd card!
Love the Nokia 820, now think it's a bit stupid to only have 8gb internal storage. V. dissapointed. Not sure if I'm willing to do a factory reset of my phone just to play a game as I don't think you should have to wipe the contents of your life to make way for a game... Unless you're really really really really really really really really really really into it. And I'm not. I was prepared to uninstall every app I previously downladed, every photo I took, every note I had taken, even had to uninstall apps which came on the phone when I received it like Here maps and Transit and City Lens bla bla... And then I STILL didn't have 4GB of free storage internally. Is a factory reset the only way?!?!?!?!
OK, Update: It has installed but not sure how. WARNING: wear oven gloves if you have some as the phone get pretty hot.
It has installed on the INTERNAL memory, but used significantly less than the 4GB other have been throwing around on this thread. I think it used about 2 point something... perhaps 3GB at the most. I unsinstalled Real Racing, it said I didn't have enough storage blaa blaa etc then I just kinda left it and it installed. A bit weird but at least I didn't have to reset my life and delete all other functions of the phone to play it. So far so good game...