Homotopy G-algebra structure on Bredon–Illman cochain complex

Let K be a topological group. The Bredon–Illman cohomology with equivariant local coefficients of a K-space was introduced in [Quart. J. Math. Oxford (2) 47 (1996) 199]. In this paper we show that the Bredon–Illman cochain complex defining the above cohomology admits a homotopy G-algebra structure as introduced in [Internat. Math. Res. Notices 3 (1995) 141]. As a consequence, we derive a B∞-algebra structure on the cochain complex.