We explain how multiplicative bundle gerbes over a compact, connected and
simple Lie group $G$ lead to a certain fusion category of equivariant bundle
gerbe modules given by pre-quantizable Hamiltonian $LG$-manifolds arising from
Alekseev-Malkin-Meinrenken's quasi-Hamiltonian $G$-spaces. The motivation comes
from string theory namely, by generalising the notion of $D$-branes in $G$ to
allow subsets of $G$ that are the image of a $G$-valued moment map we can
define a `fusion of $D$-branes' and a map to the Verlinde ring of the loop
group of $G$ which preserves the product structure. The idea is suggested by
the theorem of Freed-Hopkins-Teleman. The case where $G$ is not simply
connected is studied carefully in terms of equivariant bundle gerbe modules for
multiplicative bundle gerbes.