We prove that the comparison map from G-fixed points to G-homotopy fixed points, for the G-fold smash power of a bounded below spectrum B, becomes an equivalence after p-completion if G is a finite p-group and H-*(B; F-p) is of finite type. We also prove that the map becomes an equivalence after I(G)-completion if G is any finite group and p(*)(B) is of finite type, where I(G) is the augmentation ideal in the Burnside ring.
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