  Let $G$ be a complex connected reductive algebraic group and let
$G_{\mathbb{R}}$ be a real form of $G$. We construct a sequence of functors
$L_i\mathcal{R}$ from admissible (resp. finite-length) representations of $G$
to admissible (resp. finite-length) representations of $G_{\mathbb{R}}$. We
establish many basic properties of these functors, including their behavior
with respect to infinitesimal character, associated variety, and restriction to
a maximal compact subgroup. We deduce that each $L_i\mathcal{R}$ takes
unipotent representations of $G$ to unipotent representations of
$G_{\mathbb{R}}$. Taking the alternating sum of $L_i\mathcal{R}$, we get a
well-defined homomorphism on the level of characters. We compute this
homomorphism in the case when $G_{\mathbb{R}}$ is split.
