On The Simplicity of Reduced Crossed Products, and Stabilizers

For a minimal action of a countable group G on a compact space X, we establish necessary conditions for the simplicity of the corresponding reduced crossed product C*-algebras in terms of stabilizer subgroups. In particular, our result gives a complete characterization of the simplicity of the reduced crossed product associated with minimal actions of linear groups, answering a question of Ozawa (2014) for these groups. Joint work with Mehrdad Kalantar