Abstract
We present type-independent computations of the K O \mathrm {KO} -groups of full flag varieties, i.e. of quotient spaces G / T G/T of compact Lie groups by their maximal tori. Our main tool is the identification of the Witt ring, a quotient of the K O \mathrm {KO} -ring, of these varieties with the Tate cohomology of their complex K \mathrm {K} -ring. The computations show that the Witt ring is an exterior algebra whose generators are determined by representations of G G .
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