Normality in group rings

Abstract:

Let $KG$ be the group ring of a group $G$ over a commutative ring $K$ with unity. The rings $KG$ are described for which $xx^\sigma =x^\sigma x$ for all $x=\sum _{g\in G}\alpha _gg\in KG$, where $x\mapsto x^\sigma =~\sum _{g\in G}\alpha _gf(g)\sigma (g)$ is an involution of $KG$; here $f: G\to U(K)$ is a homomorphism and $\sigma$ is an antiautomorphism of order two of $G$.