Lemma 42.32.3. Let $(S, \delta )$ be as in Situation 42.7.1. Let $X$ be locally of finite type over $S$. Let $(\mathcal{L}, s, i : D \to X)$ be a triple as in Definition 42.28.1. Then the rule that to $f : X' \to X$ assigns $(i')^* : \mathop{\mathrm{CH}}\nolimits _ k(X') \to \mathop{\mathrm{CH}}\nolimits _{k - 1}(D')$ where $D' = D \times _ X X'$ is a bivariant class of degree $1$.

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