Equivariant and nonequivariant module spectra

by J.P. May

Abstract: Let $G$ be a compact Lie group, let $R_G$ be a commutative 
algebra over the sphere $G$-spectrum $S_G$, and let $R$ be its underlying 
nonequivariant algebra over the sphere spectrum $S$. When $R_G$ is split 
as an algebra, as holds for example for $R_G=MU_G$, we show how to 
``extend scalars'' to construct a split $R_G$-module $R_G\sma_R M$ from 
an $R$-module $M$. This allows the wholesale construction of highly 
structured equivariant module spectra from highly structured nonequivariant 
module spectra. In particular, it applies to construct $MU_G$-modules from 
$MU$-modules and therefore gives conceptual constructions of equivariant 
Brown-Peterson and Morava $K$-theory spectra.