Structure of Normal Twisted Group Rings

Let KλG be the twisted group ring of a group G over a commutative ring K with 1, and let λ be a factor set (2-cocycle) of G over K. Suppose f : G → U(K) is a map from G onto the group of units U(K) of the ring K satisfying f(1) = 1. If x = P g∈G αgug ∈ KλG then we denote P g∈G αgf(g)u −1 g by x f and assume that the map x → x is an involution of KλG. In this paper we describe those groups G and commutative rings K for which KλG is f -normal, i.e. xx f = xx for all x ∈ KλG.