Lemma 63.15.7. Let $P$ be a $\Lambda [\Gamma ]$-module, finite and projective as a $\Lambda [G]$-module, and $\gamma \in \Gamma$. Then

$\text{Tr}_{\Lambda }(\gamma , P) = \# Z_\gamma \cdot \text{Tr}_\Lambda ^{Z_\gamma }\left(\gamma , P\right).$

Proof. This follows readily from Lemma 63.15.3. $\square$

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