R-equivalence and special unitary groups

A norm homomorphism for the group of R-equivalence classes of all simply connected semisimple classical algebraic groups is constructed. The group of R-equivalence classes for special unitary groups SU(B, tau) is computed. It is proved that the variety of SU(B, tau) is rational if ind(B) less than or equal to 3 and the stable birational type of SU(B, tau) depends only on the Brauer class of B and does not depend on the involution tau. (C) 1998 Academic Press.