  Adopting a purely group-theoretical point of view, we consider the star
product of functions which is associated, in a natural way, with a square
integrable (in general, projective) representation of a locally compact group.
Next, we show that for this (implicitly defined) star product explicit formulae
can be provided. Two significant examples are studied in detail: the group of
translations on phase space and the one-dimensional affine group. The study of
the first example leads to the Groenewold-Moyal star product. In the second
example, the link with wavelet analysis is clarified.
