Involutive equivalence bimodules and inclusions of C*-algebras with   Watatani index 2
  Let A be a unital C*-algebra. We shall introduce involutive A-A-equivalence bimodules and prove that any C*-algebra containing A with Watatani index 2 is constructed by an involutive A-A-equivalence bimodule. 
K. Kodaka and T. Teruya