Picard groups of irrational rotation C*-algebras

Let a be an irrational number in [0, 1] and Ag the corresponding irrational rotation C*-algebra. Let Aut (AB) be the group of all automorphisms of Ag and Int (As) the normal subgroup of Aut(AB) Of all inner automorphisms of A(theta) Let Pic(A(theta)) be the Picard group of A(theta) In the present note we shall show that if a is not quadratic, then Pic(A(theta)) congruent to Aut(A(theta))/Int(A(theta)) and that if theta is quadratic, then Pic(A(theta)) is isomorphic to a semidirect product of Aut(A(theta))/Int(A(theta)) with Z. Furthermore, in the last section wt: shall discuss Picard groups of certain Cuntz algebras.