Group rings whose symmetric elements are Lie nilpotent

Let FG be the group ring of a group G over a field F, with characteristic d ifferent from 2. Let * denote the natural involution on FG sending each gro up element to its inverse. Denote by (FG)(+) the set of symmetric elements with respect to this involution. A paper of Giambruno and Sehgal showed tha t provided G has no 2-elements, if (FG)(+) is Lie nilpotent, then so is FG. In this paper, we determine when (FG)(+) is Lie nilpotent, if G does conta in 2-elements.