A characterization of amenability of group actions on $C^\ast$-algebras
  We show that coincidence of the full and reduced crossed product $C^\ast$-algebras of a group action on a unital commutative $C^\ast$-algebra implies amenability of the action whenever the group is exact. This is a partial answer to a problem posed by C. Anantharaman-Delaroche in 1987. 
Masayoshi Matsumura
math.OA