Let $K$ be a local field, $G$ a (connected) reductive $K$-group, and $P \le G$ a parabolic subgroup. Is the map $G(K) \rightarrow (G/P)(K)$ necessarily surjective, and, if so, then why?



Is $G \rightarrow G/P$ surjective on $K$-points over a local field?
The map G(K) to (G/P)(K) is surjective over any field K. Here is a link to an explanation by Brian Conrad.
<http://math.stanford.edu/~conrad/249CS13Page/handouts/parsurj.pdf>


