The Halacha discusses whether a Jew is permitted to rent a store to a non-Jew, who will operate on Shabbat. If the Jew is merely renting him the physical space, but the merchandise and the name on the store belong to the Non-Jew, it is permitted. The reason is that the Jew does not receive any profit from the store and the rental is on a monthly basis. There is also no issue of Marit Ayin, since the Non-Jew’s name is out front, and everybody knows that it is normal practice to rent stores today.
However, it is prohibited to operate a store on Shabbat by merely hiring a Non-Jewish manager. Since all of the merchandise and revenue belong to the Jewish owner, the Non-Jew is nothing more than the agent of the Jew. It is tantamount to the Jew himself operating his store.
What would be the Halacha if the Jew would give the non-Jewish manager a percentage of the profit? Since he has an incentive to work for himself, he is not considered the agent of the Jew. However, Hacham David Yosef writes in the sefer Amira L’akum (p.21) that this arrangement presents a problem of Mar’it Ayin. Although the formula of percentages is correct, people will see the store open and conclude that the Jew is the operator. They have no way of knowing about the percentage agreement. The only time such an arrangement would be permitted is a neighborhood or city in which there are no Jews within the Techum Shabbat (Boundaries of Shabbat).
SUMMARY
It is permitted to rent a store to a Non-Jew on a monthly basis, provided that the merchandise belongs to the non-Jew and only his name is associated with the store.
It is prohibited to hire a Non-Jew to Manage a Jewishly owned store on Shabbat.
If the Non-Jewish manager receives a percentage of the revenue, it would be permitted for him to operate a Jewish store, only in a locale in which there are no Jews.
