Extension of semistable principal bundles in positive characteristic

In 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 this instability can be bounded by a constant independent of the semistable bundles. As a consequence of this the boundedness of the set of isomorphism classes of $G$-bundles with fix degree and Chern classes is proven.