Holomorphic bundles on 2-dimensional noncommutative toric orbifolds

We define the notion of a holomorphic bundle on the noncommutative toric orbifold T θ/G associated with an action of a finite cyclic group G on an irrational rotation algebra. We prove that the category of such holomorphic bundles is abelian and its derived category is equivalent to the derived category of modules over a finite-dimensional algebra ∧. As an application we finish the computation of K 0-groups of the crossed product algebras describing the above orbifolds initiated in [18], [29], [30], [12] and [13]. Also, we describe a torsion pair in the category of ∧-modules, such that the tilting with respect to this torsion pair gives the category of holomorphic bundles on T θ/G.