In this talk we are consider free actions of a group on a separated graph and explain how this structure reflects on the level of their associated C*-algebras.

We first give a structure theorem for free actions on separated graphs, proving that all those separated graphs are skew products of the group with a certain labeling function to another separated graph, the orbit separated graph. We then explain how to recover the C*-algebra of such separated graphs as a crossed product by a coaction associated to the labeling function. Moreover, we describe the spectral decomposition of those coactions providing in this way a Fell bundle structure for their C*-algebras. All this works for full and reduced C*-algebras of separated graphs.

We first give a structure theorem for free actions on separated graphs, proving that all those separated graphs are skew products of the group with a certain labeling function to another separated graph, the orbit separated graph. We then explain how to recover the C*-algebra of such separated graphs as a crossed product by a coaction associated to the labeling function. Moreover, we describe the spectral decomposition of those coactions providing in this way a Fell bundle structure for their C*-algebras. All this works for full and reduced C*-algebras of separated graphs.