Let ${\bf{G}}$ be a reductive algebraic group defined over a number field $K$ , and let $S$ be a finite set of valuations of $K$ containing all archimedean ones. Let $G = \prod_{v \in S}{\bf{G}}(K_v)$ , and let $\Gamma$ be an $S$ -arithmetic subgroup of $G$ . Let $R \subset S$ and $T_R = \prod_{v \in R}T_v$ , where each $T_v$ is a torus of ${\bf{G}}(K_v)$ of maximal $K_v$ -rank. We prove that if $G/\Gamma$ admits a closed $T_R\pi(g)$ -orbit, then either $R = S$ or $R$ is a singleton, and we describe the closed $T_R$ -orbits in both cases. We apply this result to prove that if a collection of decomposable homogeneous forms $f_v \in K_v[x_1, \ldots, x_n], v \in S,$ takes discrete values at ${\stylefont O}^n$ , where ${\stylefont O}$ is the ring of $S$ -integers of $K$ , then there exists a homogeneous form $g \in {\stylefont O}[x_1, \ldots, x_n]$ such that $f_v = \alpha_v g$ , $\alpha_v \in K_v^*$ , for all $v \in S$ . Our result is also new in the simplest case of one real homogeneous form when $K = {\mathbb {Q}}$ and ${\stylefont O} = {\mathbb{Z}}$