Calm\`es and Fasel have shown that the twisted Witt groups of split flagvarieties vanish in a large number of cases. For flag varieties overalgebraically closed fields, we sharpen their result to an if-and-only-ifstatement. In particular, we show that the twisted Witt groups vanish in manypreviously unknown cases. In the non-zero cases, we find that the twisted totalWitt group forms a free module of rank one over the untwisted total Witt group,up to a difference in grading. Our proof relies on an identification of the Witt groups of flag varietieswith the Tate cohomology groups of their K-groups, whereby the verification ofall assertions is eventually reduced to the computation of the (twisted) Tatecohomology of the representation ring of a parabolic subgroup.
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