In this talk, we first recall the   notion of generalized tracial approximation introduced several years ago. This   notion generalizes both tracial approximation and Phillips's centrally large   subalgebras. We give some hereditary properties of generalized tracial   approximation C*-algebras. Some results are new, and some results were   obtained previously. Next, we focus on the structure of crossed products by   finite group actions with the weak tracial Rokhlin property. Let  be an infinite-dimensional simple unital   C*-algebra with stable rank one, and let  be an action of a finite group  on  with the weak tracial Rokhlin property.   Phillips asked whether the crossed product C* has stable rank one. We give an affirmative   answer to this question under the assumption that A is separable and has   strict comparison. Last, we introduce the notion of weak tracial Rokhlin   property for compact group actions on simple unital C*-algebras and give some   preservation results.