Projectivity of modules over Fourier algebras
  In this paper we will study the homological properties of various natural modules associated to the Fourier algebra of a locally compact group. In particular, we will focus on the question of identifying when such modules will be projective in the category of operator spaces. We will show that projectivity often implies that the underlying group is discrete and give evidence to show that amenability also plays an important role. 
Brian E. Forrest, Hun Hee Lee, Ebrahim Samei