  We study the Hitchin map for $G_{\mathbb{R}}$-Higgs bundles on a smooth
curve, where $G_{\mathbb{R}}$ is a quasi-split real form of a complex reductive
algebraic group $G$. By looking at the moduli stack of regular
$G_{\mathbb{R}}$-Higgs bundles, we prove it induces a banded gerbe structure on
a slightly larger stack, whose band is given by sheaves of tori. This
characterization yields a cocyclic description of the fibres of the
corresponding Hitchin map by means of cameral data. According to this, fibres
of the Hitchin map are categories of principal torus bundles on the cameral
cover. The corresponding points inside the stack of $G$-Higgs bundles are
contained in the substack of points fixed by an involution induced by the
Cartan involution of $G_{\mathbb{R}}$. We determine this substack of fixed
points and prove that stable points are in correspondence with stable
$G_{\mathbb{R}}$-Higgs bundles.
