This talk is a report on some joint work with Helene Esnault. We showed that on a smooth quasi-projective variety over the algebraic closure of a finite field, with trivial etale fundamental group, all stratified vector bundles are trivial, provided the variety admits a normal compactification with codimension 2 boundary. I will give some background, and discuss the steps going into the proof, one of which is a variant of the Grothendieck LEFF condition due to J.-B. Bost.