Abstract
We prove a structure theorem for relative coarse space morphisms from smooth Deligne–Mumford stacks, showing that each such map can be decomposed in terms of root stack and canonical stack morphisms. We explain how our result can be understood locally in terms of pseudo-reflections. Lastly, we give an application to equivariant |$K$|-theory, give several examples illustrating our result, and pose some related questions.
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