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The Witt ring of a complex flag variety describes the interesting -- i.e.torsion -- part of its topological KO-theory. We show that for a large class offlag varieties, these Witt rings are exterior algebras, and that the degrees ofthe generators can be determined by Dynkin diagram combinatorics. Besides fullflag varieties, projective spaces, and other varieties whose Witt rings werepreviously known, this class contains many flag varieties of exceptional types.Complete results are obtained for flag varieties of types G2 and F4. Theresults also extend to flag varieties over other algebraically closed fields

The Witt rings of many flag varieties are exterior algebras