More examples of non-rational adjoint groups

In this paper, we give a recursive construction to produce examples of quadratic forms qnqn in the n  -th power of the fundamental ideal in the Witt ring whose corresponding adjoint groups PSO(qn)PSO(qn) are not stably rational. Computations of the R-equivalence classes of adjoint classical groups by Merkurjev are used to show that these groups are not R-trivial. This extends earlier results of Merkurjev and Gille where the forms considered have non-trivial and trivial discriminants respectively.