On the Brauer group of a semisimple algebraic group

Let k be a field with algebraic closure (k) over bar. G a semisimple algebraic k-group, and T subset of G x (k) over bar a maximal torus with character group X(T). Denote Lambda the abstract weight lattice of the roots system of G, and by Br-n(k) and Br-n(G) the n-torsion subgroup of the Brauer group of k and G, respectively. We prove that if char k does not divide n and n is prime to the order of Lambda/X (T) then the natural homomorphism Br-n(k) -> Br-n(G) is an isomorphism. (C) 2008 Elsevier Inc. All rights reserved.