Lemma 81.29.1. In Situation 81.2.1 let $X/B$ be good. Let $\mathcal{E}$ be a finite locally free sheaf of rank $r$ on $X$. Let $\mathcal{L}$ be an invertible sheaf on $X$. Then we have

in $A^*(X)$.

Lemma 81.29.1. In Situation 81.2.1 let $X/B$ be good. Let $\mathcal{E}$ be a finite locally free sheaf of rank $r$ on $X$. Let $\mathcal{L}$ be an invertible sheaf on $X$. Then we have

81.29.1.1

\begin{equation} \label{spaces-chow-equation-twist} c_ i({\mathcal E} \otimes {\mathcal L}) = \sum \nolimits _{j = 0}^ i \binom {r - i + j}{j} c_{i - j}({\mathcal E}) c_1({\mathcal L})^ j \end{equation}

in $A^*(X)$.

**Proof.**
The proof is identical to the proof of Chow Homology, Lemma 42.39.1 replacing the lemmas used there by Lemmas 81.26.9 and 81.28.1.
$\square$

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