  Inspired by tau-tilting theory [AIR], we introduce the notion of nu-stable
support tau-tilting modules. For any finite dimensional selfinjective algebra
{\Lambda}, we give bijections between two-term tilting complexes in Kb(proj
{\Lambda}), nu-stable support tau-tilting {\Lambda}-modules and nu-stable
functorially finite torsion classes in mod {\Lambda}. Moreover, these objects
correspond bijectively to selfinjective cluster tilting objects in C if
{\Lambda} is a 2-CY tilted algebra associated with a Hom-finite 2-CY
triangulated category C. As an application, we give a necessary condition such
that selfinjective algebras are 2-CY tilted.
