Amenability of crossed products ofC*-algebras

It is shown that the class of amenable (resp. strongly amenable)C*-algebras is closed under the process of taking crossed products with discrete amenable groups. Under certain circumstances, amenability is also preserved under taking a crossed product with an amenable semigroup of linear endomorphisms. These facts are used to show that certain simpleC*-algebras studied by J. Cuntz are amenable but not strongly amenable (thus answering a question of B. E. Johnson), yet are stably isomorphic to strongly amenable algebras.Partially supported by NSF