Let $k$ be a field of characteristic zero and let $G$ be an adjoint semi-simple algebraic group over $k$.

On p34 of the paper "Sansuc - Groupe de Brauer et arithmétique des groupes algébriques lineaires sur um corps de nombres", it is claimed that there exists a collection of finite field extensions $k \subset k_i$ such that $$G \cong \prod_i \mathrm{R}_{k_i/k}(G_i) \quad (*)$$ where the $G_i$ are absolutely simple adjoint groups over $k_i$ and $\mathrm{R}_{k_i/k}$ denotes the Weil restriction.

I was quite surprised when I saw this, as it certainly seems to be something special about adjoint groups. However, Sansuc unfortunately gives no explanation nor reference why this holds.

Why does the stated isomorphism (*) exist?

I would be happy with either a proof or a reference.