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