It is permitted to buy a house in the land of Israel from a non-Jew on Shabbat, and to sign (by the non-Jew’s proxy) and arrange everything.
Shulchan Aruch 307:12
Why, might you ask, would something such as this be permitted? Even if it’s not OK to tell a gentile to do something on Shabbat that is, for a Jew, a d’Oraita prohibition (ie generated from something prohibited in the Torah), which writing on Shabbat is, if it’s to fulfill a mitzvah (inhabiting Eretz Yisrael) AND said gentile writes your name in “your language”, ie not the leshon kadosh (Hebrew) but rather English, or Russian, or Swahili, or whatever, he’s only doing a d’Rabbanan prohibition (that is, something that was decreed not-doable by a Jew on Shabbat by the later Rabbinic folk), so it’s a further-removed issue (shevut d’shevut). This of course presumes that money’s not changing hands, but still.
This, ladies and germs, is my religion. If there are any gentiles out there who are interested in selling me a house, we can do the deal this coming Shabbos. Oh, wait–I still don’t have my wallet.
aah… but remember, it must be in eretz Yisrael. a Gentile can not sell you a house in Bavel (or New York or Los Angeles or Washington) on Shabbat. Only in the Land of Israel, whether Tel Aviv or Schem/Nablus.