Operations on Ring Structures Preserved by Normalized Automorphisms of Group Rings

Let be a commutative ring, and suppose σ is a normalized -algebra automorphism of the group ring Gof a finite groupGover . In this paper we consider the action of σ on various algebraic structures associated toG. Suppose is an integral domain of characteristic 0, and that no prime divisor of the order ofGis invertible in . We show that σ preserves the λ-ring structure of G0(kG) whenkis a field with a ring homomorphism → k. If is the ring of integers of a number field, we show that σ preserves the G 0( G)-module structure of the class group Cl( G) of G, where G 0( G) is the Grothendieck group of G-lattices.