Quasitoric orbifolds are generalizations of smooth projective toric varieties. The class of quasitoric orbifolds contains orbifolds that are neither complex nor almost complex. In the paper under review the author provides a canonical Hodge structure for quasitoric orbifolds and defines their Hodge numbers. In particular, he is interested in the orbifold Hodge number conjecture, which states that the \((p,q)\)-th orbifold Hodge numbers of a Gorenstein (also known as \(\text{SL}\)) algebraic orbifold and its partial crepant resolution are equal. The main result of the paper says that the orbifold Hodge numbers of a quasi-\(\text{SL}\) quasitoric orbifold are preserved by crepant blowdowns and blowups, and hence also by crepant resolutions. The proof is motivated by the proof of the strong McKay correspondence in [V. V. Batyrev and D. I. Dais, Topology 35, No. 4, 901–929 (1996; Zbl 0864.14022)].