R-EQUIVALENCE AND NORM PRINCIPLE IN GALOIS COHOMOLOGY

Let lambda: G --> G by a k-isogeny of connected semi-simple algebraic groups defined over a field k and let C(lambda)(k) be the abelian group G(k)/lambda(G(k)). Let L/k be a finite extension of fields. We give sufficient conditions (for example, the k-rationality of the adjoint group of G) for the existence of a norm map from C(lambda)(L) to C(lambda)(k).