Hornotopy fixed points for LK (n) (En ∧ X) using the continuous action

Let K (n) be the nth Morava K-theory spectrum. Let E-n be the Lubin-Tate spectrum, which plays a central role in understanding L-K(n)(S-0), the K(n)-local sphere. For any spectrum X, define E-V(X) to be L-K(n)(E-n boolean AND X). Let G be a closed subgroup of the profinite group G(n), the group of ring spectrum automorphisms of E-n in the stable homotopy category. We show that E-V(X) is a continuous G-spectrum, with homotopy fixed point spectrum (E-V(X))(hG). Also, we construct a descent spectral sequence with abutment pi(*) ((E-V(X))(hG)). (c) 2005 Elsevier B.V. All rights reserved.