What is the ruling on a bank financing a customer's car purchase, then the bank issuing a check in the name of the car's owner, after which the car's owner offers to sell the car to the customer for a lower price, so that the customer can use the money to pay off various debts and buy another car?

If the bank's role in the transaction is merely to pay the price to the seller, and then recover it from you in installments with interest, then this is usury itself, and the transaction is void. However, if the bank actually buys the car, owns it, and takes possession of it, then sells it to you for more than it purchased it for, then this is permissible in this manner. If the sale takes place between you and the bank, and the car becomes your property and you take possession of it, then it is permissible to sell it to the original seller, provided there is no prior collusion. It is better to sell it to another person to avoid suspicion.