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quasi-affine-ness

Let $G$ be a group. Let $H$ be a subgroup of $R_u(G)$. Then $G/H\rightarrow G/R_u(G)$ is a $R_u(G)/H$ fibration. It is well known that $R_u(G)/H=\mathbb{A}^n$. Is $G/H$ an affine variety?

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