  We prove a multiplicative version of the equivariant Barratt-Priddy-Quillen
theorem, starting from the additive version proven in arXiv:1207.3459. The
proof uses a multiplicative elaboration of an additive equivariant infinite
loop space machine that manufactures orthogonal $G$-spectra from symmetric
monoidal $G$-categories. The new machine produces highly structured associative
ring and module $G$-spectra from appropriate multiplicative input. It relies on
new operadic multicategories that are of considerable independent interest and
are defined in a general, not necessarily equivariant or topological, context.
Most of our work is focused on constructing and comparing them. We construct a
multifunctor from the multicategory of symmetric monoidal $G$-categories to the
multicategory of orthogonal $G$-spectra. With this machinery in place, we prove
that the equivariant BPQ theorem can be lifted to a multiplicative equivalence.
That is the heart of what is needed for the presheaf reconstruction of the
category of $G$-spectra in arXiv:1110.3571.
