  In this paper we will demonstrate that any compact quantum group can be used
as symmetry groups for quantum channels, which leads us to the concept of
covariant channels. We, then, unearth the structure of the convex set of
covariant channels by identifying all extreme points under the assumption of
multiplicity-free condition for the associated fusion rule, which provides a
wide generalization of some recent results. The presence of quantum group
symmetry contrast to the group symmetry will be highlighted in the examples of
quantum permutation groups and $SU_q(2)$. In the latter example, we will see
the necessity of the Heisenberg picture coming from the non-Kac type condition.
This paper ends with the covariance with respect to projective representations,
which leads us back to Weyl covariant channels and its fermionic analogue.
