Let $G$ and $H$ be affine algebraic groups over a scheme $S$ of characteristic 0 and let $\textbf{Hom}_{S,gp}(G,H)$ be the functor $T \mapsto \text{Hom}\_{T,gp}(G,H)$ > **Theorem** (SGA 3, expose XXIV, 7.3.1(a)): Suppose G is reductive. Then $\textbf{Hom}_{S,gp}(G,H)$ is representable by a scheme. Can this fail if $G$ is not reductive? I worked out a few example with $G = \mathbb{G}_a$, but they were representable.