  Let $\mathbf{G}$ be a connected reductive complex algebraic group with split
real form $(G,\sigma)$. Consider a strict wonderful $\mathbf{G}$-variety
$\bf{X}$ equipped with its $\sigma$-equivariant real structure, and let $X$ be
the corresponding real locus. Further, let $E$ be a real differentiable
$G$-vector bundle over $X$. In this paper, we introduce a distribution
character for the regular representation of $G$ on the space of smooth sections
of $E$, and show that on a certain open subset of $G$ of transversal elements
it is locally integrable and given by a sum over fixed points.

Algebraic Geometry