Abstract
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.
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