Equivariant p-adic homotopy theory

Let G be a finite group. We show that the cochain functor with coefficients in Fp gives an equivalence between the p-adic equivariant homotopy category of finite type nilpotent G-spaces and a full subcategory of the homotopy category of diagrams of E∞ Fp-algebras indexed on the orbit category of G. This turns out to be an easy consequence of Elmendorfʹs Theorem and Kanʹs work on diagrams in closed model categories plus the equivalence in the nonequivariant context.