Let $G$ be a locally compact group and let $K$ be a compact group. Let $(\tau, V_\tau)$ be an irreducible representation of $K$.
We consider the space of $Endo_K(\tau)$-valued, compactly supported continuous functions
$f$ on $G$
with $$ f(k_1 g k_2) = \tau(k_1) f(g) \tau(k_2), $$ which is an $*$ algebra under convolution.
What is a good reference for such algebras, especially in the context with reductive group over local fields and the connection to representation theory?