  We associate a rigid C*-tensor category $C$ to a totally disconnected locally
compact group $G$ and a compact open subgroup $K < G$. We characterize when $C$
has the Haagerup property or property (T), and when $C$ is weakly amenable.
When $G$ is compactly generated, we prove that $C$ is essentially equivalent to
the planar algebra associated by Jones and Burstein to a group acting on a
locally finite bipartite graph. We then concretely realize $C$ as the category
of bimodules generated by a hyperfinite subfactor.
