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It is a "well known" fact that locally free sheaves over a Stein space $X$ are projective as $\mathcal{O}_X$-modules (see e.g. just after Lemma 1.6 in O'Brian-Toledo-Tong's "The trace ...

Let $i:X\to Y$ be a closed embedding of Stein spaces, $G$ be a coherent $O_Y$-module. Set $I=\ker(i^*:O(Y)\to O(X))$. Then $I$ is an ideal of the ring $O(Y)$. Is that true that $\Gamma(X,i^*G)=G(Y)/...