In this paper we consider a class of exactly solvable closed string flux backgrounds that exhibit non-commutativity in the closed string coordinates. They are realized in terms of freely-acting asymmetric Z N -orbifolds, which are themselves close relatives of twisted torus fibrations with elliptic Z N -monodromy (elliptic T-folds). We explicitly construct the modular invariant partition function of the models and derive the non-commutative algebra in the string coordinates, which is exact to all orders in α ′ . Finally, we relate these asymmetric orbifold spaces to inherently stringy Scherk-Schwarz backgrounds and nongeometric fluxes.

We compute instantonic effects in globally consistent T 6 /Z 2 × Z 2 orientifold models with discrete torsion and magnetised D-branes. We consider fractional branes and instantons wrapping the same rigid cycles. We clarify and analyse in detail the lowenergy effective action on D-branes in these models. We provide explicit examples where instantons induce linear terms in the charged fields, or non-perturbative mass terms are generated. We also find examples where the gauge theory on fractional branes has conformal symmetry at one-loop, broken by instantonic mass terms at a hierarchically small energy scale.