Let $O=k[[\pi]]$ and $F=k((\pi))$ and $G\rightarrow GL_{n}$ a faithful representation.
Let $A, B\in G(O)\cap G(F)^{rs}$ (rs for regular semisimple)) such that there exists $g\in GL_{n}(O)$ such that
$gAg^{-1}=B$,
does it exist an element $g_{1}\in G(O)$ such that $g_{1}Ag_{1}^{-1}=B$?