Outer Automorphisms Of Adjoint Groups Of Type D And Nonrational Adjoint Groups Of Outer Type A

For a classical group G of type D-n over a field k of characteristic different from 2, we show the existence of a finitely generated regular extension of k over which G admits outer automorphisms. Using this result and a construction of groups of type A from groups of type D, we construct new examples of groups of type (2)A(n) with n equivalent to 3 mod 4 and the first examples of type (2)A(n) with n equivalent to 1 mod 4 ( n >= 5) that are not R-trivial, hence not rational (nor stably rational).