Let $G$ be a simply connected semisimple algebraic $K$-group and $K$ be a finite extension of $k$. 
Is $R\_{K/k}G$ still a simply connected algebraic group?


We say $G$ is simply connected if for any central isogeny $G'\to G$ is in fact an isomorphism of algebraic groups. 



Is restriction of scalars of simply connected algebraic groups still SC?
May I assume that $K/k$ is separable?


Let $T$ be a maximal torus in $G$. Since $G$ is simply connected, the weight lattice and character lattice for $T$ are the same. This remains true if we replace $G$ by a direct product of $[K:k]$ copies of $G$, and $T$ by a corresponding product of tori. Over the algebraic closure, our direct product is isomorphic to $R\_{K/k}G$. Our condition on the lattices doesn't depend on the rational structure of an algebraic group, so this latter group is also simply connected.


