  If $\mathcal{F}$ is a saturated fusion system on a finite $p$-group $S$, we
define the Chern subring $Ch(\mathcal{F})$ of $\mathcal{F}$ to be the subring
of the mod-$p$ cohomology $H^*(S)$ of $S$ generated by the Chern classes of
$\mathcal{F}$-stable representations of $S$. We show that $Ch(\mathcal{F})$ is
contained in $H^*(\mathcal{F})$ and apply a result of Green and the first
author to describe its spectrum in terms of a certain category of elementary
abelian subgroups of $S$. We obtain similar results for various related
subrings, including those generated by characteristic classes of
$\mathcal{F}$-stable $S$-sets.
