The author considers a group of agents, each of whom initially owns an indivisible object (e.g., a house, or a university apartment). The problem is to reallocate the objects in such a way that everyone receives one object. The class of mechanisms (social choice functions) that are strategy-proof, ex post individually rational, ex post budget balanced and collusion-proof is characterized. The mechanisms are intuitive and straightforward to implement in practice. In these mechanisms, the price of each object is fixed in advance. Each agent pays the price of the object he receives to the initial owner. The transfer scheme reduces the economy to a Shapley-Scarf economy without money, where an agent's valuation for an object is equal to his true valuation minus the price of the object. The Shapley-Scarf economy having an unique core assignment (for generic type profiles), this core assignment is the selected solution.