Is it permitted for a Jew to communicate in real time, conducting business, with a non-Jew who is in a time zone where Shabbat has already arrived, assuming it's not yet Shabbat where the Jew is? Assume that this would entail both parties' performance of melachot during the communication, and requests from the Jew to the non-Jew to do further melachot immediately after the communication.
I know there's a general rule against asking a non-Jew to perform melachot on Shabbat, and another rule against benefiting from melachot he does for a Jew on Shabbat. But I don't know whether that refers to Shabbat in his time zone or in mine.
