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How to compute the transfer maps for G-theory of Noetherian schemes

If $\tilde{X}$ is the total space of a line bundle $L$ and $i \colon \mathbb{P}^1 \to \tilde{X}$ is the embedding of the zero section there is an exact sequence $$ 0 \to p^* L^\vee \to \mathcal{O}_{\...
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