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 $\Gamma(X,i^*G)=G(Y)/IG(Y)$? I don't even know if $G(Y)/IG(Y)$ is a Stein module over the Stein algebra $O(X)=O(Y)/I$.
In the algebraic setting, when $i$ is a closed immersion between affine schemes, an analog holds. This leads to the question above.
