  The Dunkl operators associated to a necessarily finite Coxeter group acting
on a Euclidean space are generalized to any finite group using the techniques
of non-commutative geometry, as introduced by the authors to view the usual
Dunkl operators as covariant derivatives in a quantum principal bundle with a
quantum connection. The definitions of Dunkl operators and their corresponding
Dunkl connections are generalized to quantum principal bundles over quantum
spaces which possess a classical finite structure group. We introduce cyclic
Dunkl connections and their cyclic Dunkl operators. Then we establish a number
of interesting properties of these structures, including the characteristic
zero curvature property. Particular attention is given to the example of
complex reflection groups, and their naturally generalized siblings called
groups of Coxeter type.
