  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 $\pi_*(B)$ is of finite
type, where $I(G)$ is the augmentation ideal in the Burnside ring.
