E-infinity structure in hyperoctahedral homology

Hyperoctahedral homology for involutive algebras is the theory associated to hyperoctahedral crossed simplicial group. It related equivariant stable homotopy via of infinite loop spaces. In this paper we show that there an E-infinity algebra structure on module computes homology. We deduce admits Dyer-Lashof operations. Furthermore, a Pontryagin product which gives associative, graded-commutative algebra. also give explicit description in degree zero. Combining and fails preserve Morita equivalence.