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 cursive Greek chi = Σ_g∈G α_gu_g ∈ K_λG then we denote Σ_g∈G α_gf(g)u^-1_g by cursive Greek chi^f and assume that the map cursive Greek chi → cursive Greek chi^f is an involution of KλG. In this paper we describe those groups G and commutative rings K for which K_λG is f-normal, i.e. cursive Greek chicursive Greek chi^f = cursive Greek chi^f cursive Greek chi for all cursive Greek chi ∈ K_λG.