Extension and lifting of G-bundles on stacks

Abstract

We study extension properties for morphisms of stacks of bundles for group algebraic spaces. Applications are a short proof of the classification of bundles on the projective line for smooth geometrically reductive groups and the existence of splittings of filtered fiber functors for gerbes bound by quasi-affine smooth group schemes defined over rings.

Thoroughly revised due to remarks of a referee, some results generalized to quasi-affine group schemes, to appear in Journal of the Institute of Mathematics of Jussieu