This question is highly related to some other questions that I've previously asked, especially to this one. In this problem we have a scheme $X$ and a closed subscheme $Z$ the formal completion $X_Z$. The formal vector bundles on $X_Z$ are defined as limit of vector bundles on the infinitesimal neighborhoods. This category is closed under extensions (this in itself might not be too obvious). So we can consider the exact category of formal vector bundles on $X_Z$ and define the algebraic $K$-theory of the formal scheme $X_Z$. Now my question is does the $K$-theory of formal scheme $X_Z$ satisfy Zariski descent with respect to some open affine covering? (Open affine covering is induced by some open covering of $X$.)
It might be necessary to consider with finite coefficients. For example for coefficients mod $l$, where $l$ is invertible.
