Fourier theory and C∗C∗-algebras

We discuss a number of results concerning the Fourier series of elements in reduced twisted group C∗C∗-algebras of discrete groups, and, more generally, in reduced crossed products associated to twisted actions of discrete groups on unital C∗C∗-algebras. A major part of the article gives a review of our previous work on this topic, but some new results are also included.