  Hyperoctahedral homology is the homology theory associated to the
hyperoctahedral crossed simplicial group. It is defined for involutive algebras
over a commutative ring using functor homology and the hyperoctahedral bar
construction of Fiedorowicz. The main result of the paper proves that
hyperoctahedral homology is related to equivariant stable homotopy theory: for
a discrete group of odd order, the hyperoctahedral homology of the group
algebra is isomorphic to the homology of the fixed points under the involution
of an equivariant infinite loop space built from the classifying space of the
group.
