  The Morava stabilizer groups play a dominating role in chromatic stable
ho-motopy theory. In fact, for suitable spectra X, for example all finite
spectra, thechromatic homotopy type of X at chromatic level n \textgreater{} 0
and a given prime p islargely controlled by the continuous cohomology of a
certain p-adic Lie group Gn,in stable homotopy theory known under the name of
Morava stabilizer group oflevel n at p, with coefficients in the corresponding
Morava module (En)$\star$X.

Algebraic Topology