I came up with the following question. Let us suppose that we have an affine scheme $X=\text{Spec}(A)$. It is well known that vector bundles on $X$ are equivalent to $A$-modules. In particular, if vector bundles have finite rank then the equivalence is restricted to finitely generated projective $A$-modules. Since we can understand a vector bundle as a principal $Gl$-bundle, my question is:
If we have an affine group $G\subset Gl(V)$, is there any easy description as above for principal $G$-bundles over $X$? Do you know any result in this direction?
Thank you for your time.