We compute the mod(p) homotopy groups of the continuous homotopy fixed point spectrum E_2^{ hH_2} for p>2, where E_n is the Landweber exact spectrum whose coefficient ring is the ring of functions on the Lubin-Tate moduli space of lifts of the height n Honda formal group law over F_{ p^n}, and H_n is the subgroup WF^x_{ p^n} wreath product Gal(F_{ p^n}/F_p) of the extended Morava stabilizer group G_n. We examine some consequences of this related to Brown-Comenetz duality and to finiteness properties of homotopy groups of K(n)_*-local spectra. We also indicate a plan for computing pi_*(E_n^{ hH_n} smash V(n-2)), where V(n-2) is an E_{ n*}-local Toda complex.
Categories: math.AT