  For a large class of good moduli spaces $X$ of symmetric stacks
$\mathcal{X}$, we define noncommutative motives $\mathbb{D}^{\text{nc}}(X)$
which can be regarded as categorifications of the intersection cohomology of
$X$. These motives are summands of noncommutative resolutions of singularities
$\mathbb{D}(X)\subset D^b(\mathcal{X})$ of $X$. The category $\mathbb{D}(X)$ is
a global analogue of the noncommutative resolutions of singularities of $V//G$
for $V$ a symmetric representation of a reductive group $G$ constructed by
\v{S}penko-Van den Bergh.
