I was wondering if anyone had a refrence for the fact that $K^*(BG)=K^*(BT)^W$ for $G$ a compact connected lie group, $T$ a maximal torus, and $W$ the associated Lie group. I was able to derive this fact from the corrosponding fact for the representation ring, using the Atiyah-Segal completion theorem. Does anyone have a proof of this fact that doesn't involve Atiyah-Segal?
2025-01-13 02:20:59.1736734859
Proof that $K^*(BG)=K^*(BT)^W$.
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