Weak tracial approximation and a weak Rokhlin property for C*-dynamical systems

We extend results on tracial approximability of crossed products from the setting of topological dynamical systems to C*-dynamical systems. For actions of discrete amenable groups on unital C*-algebras, we introduce a weak Rokhlin property which leads to a weak tracial approximation of the crossed products by means of finite direct sums of matrix algebras over hereditary subalgebras of the original algebra. Examples are given.