Cox construction is a central object of study for toric geometry. It provides a far-reaching generalization of the classical Hopf bundle presentation for the projective space and allows one to phrase many questions about toric varieties in the language of graded commutative algebra. Recently, we showed that the Cox construction could be considered in the more general setting of “generalized fans.” These objects, unlike the classical fans of toric geometry, do not require any separateness condition and thus allow one to encode objects more general than just toric varieties. We call these objects toric stacks. In the talk, I want to showcase one application of this approach: the calculation of automorphism groups of complex moment-angle manifolds. This class of complex manifolds includes many known examples of non-Kahler manifolds, such as Hopf and Calabi-Eckmann manifolds. The talk is based on the paper arXiv:2403.02465.