Witt invariants of Weyl groups

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We describe the Witt invariants of a Weyl group over a field k0 by giving generators for the W(k0)-module of Witt invariants, under the assumption that the characteristic of k0 does not divide the order of the group. For the Weyl groups of types Bn, Cn, Dn, and G2, we show that the Witt invariants are generated as a W(k0)-algebra by trace forms and their exterior powers, extending a result due to Serre in type An. Many of our computational methods are applicable to computing Witt invariants of any smooth linear algebraic group over k0, including a technique for lifting module generators from cohomological invariants to Witt invariants.