Hochschild and cyclic homology of the crossed product of algebraic irrational rotational algebra by finite subgroups of SL(2,Z)SL(2,Z)

Let Γ⊂SL(2,Z)Γ⊂SL(2,Z) be a finite subgroup acting on the irrational rotational algebra AθAθ via the restriction of the canonical action of SL(2,Z)SL(2,Z). Consider the crossed product algebra Aθalg⋊Γ obtained by the restriction of the Γ action on the algebraic irrational rotational algebra. In this paper we prove many results on the homology group of the crossed product algebra Aθalg⋊Γ. We also analyse the case of the smooth crossed product algebra, Aθ⋊ΓAθ⋊Γ and calculate some of its homology groups.