Here it is in a nutshell:
• The sale of chametz in Jewish-owned stores that operate fully on Pesach (i.e., chametz is sold in the store) is a matter of dispute.
• Even for those who assume the sale is valid, it is questionable whether the sale is effective for chametz that is acquired during Pesach.
• Ask your rabbi to determine which supermarkets are Jewish owned or are supplied by Jewish distributors, and how long after Pesach you must wait to purchase chametz sold in these stores.