Transfer and complex oriented cohomology rings

Abstract

For finite coverings we elucidate the interaction between transferred Chern classes and Chern classes of transferred bundles. This involves computing the ring structure for the complex oriented cohomology of various homotopy orbit spaces. In turn these results provide universal examples for computing the stable Euler classes (ie $T{r}^{\ast }\left(1\right)$) and transferred Chern classes for $p$–fold covers. Applications to the classifying spaces of $p$–groups are given.