The Halacha delineates three conditions that must be present in order for a non-Jew to perform work for a Jew on Shabbat. First, he must be Kablan, paid on a per-task basis. Second, The Jew is prohibited from instructing him to specifically perform the task on Shabbat. Finally, the task must be performed outside of the Jew’s premises.
Therefore, on may not give a check to a bank teller before Shabbat, instructing him to deposit the check on Shabbat. Although the teller is a Kablan and does not perform his work on the Jew’s premises, the Jew is prohibited from telling him to do the work specifically on Shabbat. However, one may send a check to the bank via mail on Friday, knowing that the check will arrive and be deposited on Shabbat. Since the Jew did not send the check via express mail so that it would specifically be deposited on Shabbat, it is permitted.
SUMMARY: It is prohibited to leave a check with a bank teller on Friday, instructing him to deposit the check on Shabbat.