  Let $X$ be a projective and smooth variety over an algebraically closed field
$k$. Let $f:Y\rightarrow X$ be a proper and surjective morphism of
$k$-varieties. Assuming that $f$ is separable, we prove that the Tannakian
category associated to the vector bundles $E$ on $X$ such that $f^*E$ is
trivial is equivalent to the category of representations of a finite and etale
group scheme. We give a counterexample to this conclusion in the absence of
separability.
