Symmetric units satisfying a group identity

Let K be an infinite field of characteristic p≠2, G a locally finite group and KG its group algebra. Let denote the K-linear extension of an involution φ defined on G. In this paper we prove, under some assumptions, that if the set of φ-symmetric units of KG satisfies a group identity then KG satisfies a polynomial identity. Moreover, in case the prime radical of KG is nilpotent we characterize the groups for which the φ-symmetric units satisfy a group identity.