Rigidity in equivariant stable homotopy theory

For any finite group G, we show that the 2–local G–equivariant stable homotopy category, indexed on a complete G–universe, has a unique equivariant model in the sense of Quillen model categories. This means that the suspension functor, homotopy cofiber sequences and the stable Burnside category determine all “higher-order structure” of the 2–local G–equivariant stable homotopy category, such as the equivariant homotopy types of function G–spaces. Our result can be seen as an equivariant version of Schwede’s rigidity theorem at the prime 2.