Amenable Actions on Ill-Behaved Simple C*-Algebras

By combining R & oslash;rdam's construction and the author's previous construction, we provide the first examples of amenable actions of non-amenable groups on simple separable nuclear C$<^>\ast $-algebras that are neither stably finite nor purely infinite. For free groups, we also provide unital examples. We arrange the actions so that the crossed products are still simple with both a finite and an infinite projection.