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abstract: 'In this paper we study the extension of structure group of principal bundles with a reductive algebraic group as structure group on smooth projective varieties defined over algebraically closed field of positive characteristic. Our main result is to show that given a representation $\rho$ of a reductive algebraic group $G$, there exists an integer $t$ such that any semistable $G$-bundle whose first $t$ frobenius pullbacks are semistable induces a semistable vector bundle on extension of structure group via $\rho$. Moreover we quantify the number of such frobenius pullbacks required.'
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**Rationality of the instability parabolic and related results**

**Sudarshan Gurjar, Vikram Mehta**

Introduction
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Let $X$ be a smooth projective variety defined over an algebraically closed field $k$. Fix a very ample line bundle $H$. Let $G$ be a reductive algebraic group defined over $k$. All representations considered in this paper are rational finite-dimensional representations. Recall that a $G$-bundle is semistable with respect to the polarisation $H$ if for any reduction of structure group to a parabolic subgroup $P$ and any dominant character of P, the induced line bundle on $X$ has non-positive degree.\
$~$ Now let $\rho: G \rightarrow Gl(V)$ be a rational representation of $G$ sending 