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

Remarks on the star product of functions on finite and compact groups