We have shown that the n-th Morava K–theory K*(X) for a
CW–spectrum X with action of Morava stabilizer group Gn
can be recovered from the system of some height (n+1) cohomology groups
E*(Z) with Gn+1–action indexed by finite
subspectra Z. In this note we reformulate and extend the above result.
We construct a symmetric monoidal functor F from the category of
E∨*(E)–precomodules to the category of
K*(K)–comodules. Then we show that K*(X)
is naturally isomorphic to the inverse limit of F(E*(Z))
as a K*(K)–comodule.
Dedicated to Professor Nishida on the
occasion of his 60th birthday
Keywords
Milnor operation, generalized Chern
character, Morava stabilizer group