  Using the formalism of quantizers and dequantizers, we show that the
characters of irreducible unitary representations of finite and compact groups
provide kernels for star products of complex-valued functions of the group
elements. Examples of permutation groups of two and three elements, as well as
the SU(2) group, are considered. The k-deformed star products of functions on
finite and compact groups are presented. The explicit form of the quantizers
and dequantizers, and the duality symmetry of the considered star products are
discussed.
