  When G is a profinite group and H and K are closed subgroups, with H normal
in K, it is not known, in general, how to form the iterated homotopy fixed
point spectrum (Z^{hH})^{hK/H}, where Z is a continuous G-spectrum and all
group actions are to be continuous. However, we show that, if G=G_n, the
extended Morava stabilizer group, and Z=L_{K(n)}(E_n \wedge X), where L_{K(n)}
is Bousfield localization with respect to Morava K-theory, E_n is the
Lubin-Tate spectrum, and X is any spectrum with trivial G_n-action, then the
iterated homotopy fixed point spectrum can always be constructed. Also, we show
that (E_n^{hH})^{hK/H} is just E_n^{hK}, extending a result of Devinatz and
Hopkins.
