R-Equivalence and Special Unitary Groups

A norm homomorphism for the group ofR-equivalence classes of all simply connected semisimple classical algebraic groups is constructed. The group ofR-equivalence classes for special unitary groupsSU(B, τ) is computed. It is proved that the variety ofSU(B, τ) is rational if ind(B) ≤ 3 and the stable birational type ofSU(B, τ) depends only on the Brauer class ofBand does not depend on the involution τ.