A local-global principle for similarities over function fields of p-adic curves

Let $p\in N$ be a prime with $p\ne 2$, and let K be a p-adic field. Let F be the function field of a curve over K. Let ${\Omega }_F$ be the set of all divisorial discrete valuations of F. In this paper, we ask whether the Hasse principle holds for semisimple adjoint linear algebraic groups over F. We give a positive answer to this question for a class of adjoint classical groups.