Equivariant and nonequivariant module spectra Original Research Article

Let G be a compact Lie group, let RG, be a commutative algebra over the sphere G-spectrumSG, and let R be its underlying nonequivariant algebra over the sphere spectrum S. When RG is split as an algebra, as holds, for example, for RG = MUG. we show how to “extend scalars” to construct a split RG-modale MG = RG ΛR M from an R-module M. We also show how to compute the coefficients M*G in terms of the coefficients R*G, R*, and M*. This allows the wholesale construction of highly structured equivariant module spectra from highly structured nonequivariant module spectra. In particular, it applies to construct MUG-modules from MU-modules and therefore gives conceptual constructions of equivariant Brown-Peterson and Morava K-theory spectra.