Robbins, Daniel G.Sharpe, EricVandermeulen, Thomas2022-07-282022-07-282022-02-141029-8479108http://hdl.handle.net/10919/111393In this paper, we introduce a new set of modular-invariant phase factors for orbifolds with trivially-acting subgroups, analogous to discrete torsion and generalizing quantum symmetries. After describing their basic properties, we generalize decomposition to include orbifolds with these new phase factors, making a precise proposal for how such orbifolds are equivalent to disjoint unions of other orbifolds without trivially-acting subgroups or one-form symmetries, which we check in numerous examples.application/pdfenCreative Commons Attribution 4.0 InternationalConformal Field TheoryGauge SymmetryAnomalies in Field and String TheoriesArticle - Refereedhttps://doi.org/10.1007/JHEP02(2022)1082