 
Summary: IRREDUCIBLE REPRESENTATIONS OF C*CROSSED
PRODUCTS BY FINITE GROUPS
ALVARO ARIAS AND FRŽEDŽERIC LATRŽEMOLI`ERE
Abstract. We describe the structure of the irreducible represen
tations of crossed products of unital C*algebras by actions of finite
groups in terms of irreducible representations of the C*algebras
on which the groups act. We then apply this description to derive a
characterization of irreducible representations of crossedproducts
by finite cyclic groups in terms of representations of the C*algebra
and its fixed point subalgebra. These results are applied to crossed
products by the permutation group on three elements and illus
trated by various examples.
1. Introduction
What is the structure of irreducible representations of C*crossed
products A G of an action of a finite group G on a unital C*
algebra A? Actions by finite groups provide interesting examples, such
as quantum spheres [1, 2] and actions on the free group C*algebras
[3], among many examples, and have interesting general properties, as
those found for instance in [9]. Thus, understanding the irreducible
representations of their crossedproducts is a natural inquiry, which we
