Restriction theorems for principal bundles in arbitrary characteristic

The aim of this paper is to give a proof of the restriction theorems for principal bundles with a reductive algebraic group as structure group in arbitrary characteristic. Let G   be a reductive algebraic group over any field k=k¯, let X be a smooth projective variety over k, let H be a very ample line bundle on X and let E be a semistable (resp. stable) principal G-bundle on X w.r.t. H. The main result of this paper is that the restriction of E to a general smooth curve which is a complete intersection of ample hypersurfaces of sufficiently high degrees is again semistable (resp. stable).