The Poskim discuss a case in which a Jewish company outsources its customer service to a non-Jewishly owned call-center. The question is whether the center is allowed to take calls on behalf of the Jewish company on Shabbat.
The first factor that must be ascertained is the arrangement for payment. If they are being paid on a per-hour or per-day basis, it is prohibited. In such an arrangement, the call-center acts the Jew’s agent to violate Shabbat. However, if they are paid based on call volume, they are considered a "Kablan," a per-task contractor; any work done on Shabbat is done on their own volition for their incentive to make more money.
Even if the call center is deemed a "Kablan," it is still prohibited to specifically instruct them to work on Shabbat. Rav Shlomo Miller, based on the Shulhan Aruch HaRav (Rabbi Shneur Zalman of Liadi, Russia, 1745-1813, Siman 244), ruled that such an arrangement would be permitted if the Jew makes it clear at the outset that he does not demand that the company work on Shabbat, and that they will not be held liable if they fail to offer service on Shabbat. In such a case, any work done on Shabbat is not connected with the Jew.
SUMMARY: It is permitted to hire a Non-Jewish customer service center to answer calls on Shabbat only if they are paid on a per-task basis and the Jew informs them that they are not obligated to work on Shabbat.