Computing Chow rings of twisted flag varieties for subgroups of an algebraic group

Let $G_k$ be a split algebraic group over $k$. Given a non-trivial $G_k$-torsor $G$, we consider the (twisted) flag variety $F=G\mathrm{/}{B}_k$ for the Borel subgroup $B_k$ containing in $G_k$. The purpose of this paper is the study how to compute the Chow rings $C{H}^{\ast }(F)$ for various $F$ over some extension fields $K$ of $k$.