  We describe the multiplicative structures that arise on categories of
equivariant modules over certain equivariant commutative ring spectra. Building
on our previous work on N-infinity ring spectra, we construct categories of
equivariant operadic modules over N-infinity rings that are structured by
equivariant linear isometries operads. These categories of modules are endowed
with equivariant symmetric monoidal structures, which amounts to the structure
of an "incomplete Mackey functor in homotopical categories". In particular, we
construct internal norms which satisfy the double coset formula. We regard the
work of this paper as a first step towards equivariant derived algebraic
geometry.
