2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69601In this article we study the behaviour of semistable principal $G$-bundles over a smooth projective variety $X$ under the extension of structure groups in positive characteristic. We extend some results of Ramanan-Ramanathan \cite{Ramanan-Ramanathan} on rationality of instability flags and show that the associated vector bundles via representations of $G$ are not too unstable and the instability can be bounded by a constant independent of semistable bundles. As a consequence of this the boundedness of the set of isomorphism classes of semistable $G$-bundles with fixed degree and Chern classes is proven.25 pages. To appear in the J. Reine Angew. MathAlgebraic Geometry14J60;14L24text