  We give a general framework of equivariant model category theory. Our groups
G, called Hopf groups, are suitably defined group objects in any well-behaved
symmetric monoidal category V. For any V, a discrete group G gives a Hopf
group, denoted I[G]. When V is cartesian monoidal, the Hopf groups are just the
group objects in V. When V is the category of modules over a commutative ring
R, I[G] is the group ring R[G] and the general Hopf groups are the
cocommutative Hopf algebras over R. We show how all of the usual constructs of
equivariant homotopy theory, both categorical and model theoretic, generalize
to Hopf groups for any V. This opens up some quite elementary unexplored
mathematical territory, while systematizing more familiar terrain.
