The stable Adams operations on Hermitian K-theory

Abstract

We prove that exterior powers of (skew-)symmetric bundles induce a λ-ring structure on the ring GW 0 (X) ⊕ GW 2 (X), when X is a scheme where 2 is invertible. Using this structure, we define stable Adams operations on Hermitian K-theory. As a byproduct of our methods, we also compute the ternary laws associated to Hermitian K-theory.