  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 (i.e. Tr^*(1)) and transferred Chern classes for p-fold
covers. Applications to the classifying spaces of p-groups are given.
