Abstract
In this paper, we settle an open conjecture regarding the assertion that the Euler-characteristic of G/NG(T) for a split reductive group scheme G and the normalizer of a split maximal torus NG(T) over a field is 1 in the Grothendieck-Witt ring with the characteristic exponent of the field inverted, under the assumption that the base field contains a −1. Numerous applications of this to splittings in the motivic stable homotopy category and to Algebraic K-Theory are worked out in several related papers by Gunnar Carlsson and the authors.
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