  In this note some generalization of the Chern character is discussed from the
chromatic point of view. We construct a multiplicative G_{n+1}-equivariant
natural transformation \Theta from some height (n+1) cohomology theory E^*(-)
to the height n cohomology theory K^*(-)\hat{\otimes}_F L, where K^*(-) is
essentially the n-th Morava K-theory. As a corollary, it is shown that the
G_n-module K^*(X) can be recovered from the G_{n+1}-module E^*(X). We also
construct a lift of \Theta to a natural transformation between characteristic
zero cohomology theories.
