Adams operations for projective modules over group rings, by Bernhard Koeck

Let R be a commutative ring, G a group acting on R, and k a natural number which is invertible in R. Generalizing a definition of Kervaire we construct a k-th Adams operation on the Grothendieck group and on the higher K-theory of projective modules over the twisted group ring R#G. For this we use generalizations of Atiyah's cyclic power operations and shuffle products in higher K-theory. For the Grothendieck group we show that k-th Adams operation is multiplicative and that it commutes with base change, with the Cartan homomorphism, and with the l-th Adams operation for any other l which is invertible in R.

Bernhard Koeck <>