Can a traffic stop be done on private property?

Question Details: I went to a store to get food for Thanksgiving. Once I parked in a parking spot, an officer pulled up to me with his lights on. The officer said that the reason he pulled me over was because on the way to the store I passed him and he saw that I didn't have a seatbelt on. Could he perform the traffic stop for a seatbelt violation on private property or did he have to wait until I got back in the car and left the private property?

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