  For discrete Hecke pairs $(G,H)$, we introduce a notion of covariant
representation which reduces in the case where $H$ is normal to the usual
definition of covariance for the action of $G/H$ on $c_0(G/H)$ by right
translation; in many cases where $G$ is a semidirect product, it can also be
expressed in terms of covariance for a semigroup action. We use this covariance
to characterise the representations of $c_0(G/H)$ which are multiples of the
multiplication representation on $\ell^2(G/H)$, and more generally, we prove an
imprimitivity theorem for regular representations of certain crossed products
by coactions of homogeneous spaces. We thus obtain new criteria for extending
unitary representations from $H$ to $G$.
