Let $k$ be a field of characteristic zero (I'm only interested in number fields), and let $\mathbb{G}_{/k}$ be a linear algebraic group defined over $k$ which is almost $k$-simple (all normal subgroups defined over $k$ are finite). This group need not be absolutely almost simple, and one way this situation can arise is when $\mathbb{G}$ is the Weil restriction of scalars of an almost-simple $K$-group defined over a finite extension $K/k$. Is that the only possibility?
In other words, suppose $\mathbb{G}$ is $k$-almost simple. Is there a finite extension $K$ and an absolutely almost simple group $\mathbb{H}_{/K}$ such that $R^K_k\mathbb{H}$ is $k$-isogenous to $\mathbb{G}$?