  Let E_n be the Lubin-Tate spectrum and let G_n be the nth extended Morava
stabilizer group. Then there is a discrete G_n-spectrum F_n, with L_{K(n)}(F_n)
\simeq E_n, that has the property that (F_n)^{hU} \simeq E_n^{hU}, for every
open subgroup U of G_n. In particular, (F_n)^{hG_n} \simeq L_{K(n)}(S^0). More
generally, for any closed subgroup H of G_n, there is a discrete H-spectrum
Z_{n, H}, such that (Z_{n, H})^{hH} \simeq E_n^{hH}. These conclusions are
obtained from results about consistent k-local profinite G-Galois extensions E
of finite vcd, where L_k(-) is L_M(L_T(-)), with M a finite spectrum and T
smashing. For example, we show that L_k(E^{hH}) \simeq E^{hH}, for every open
subgroup H of G.
