Geodesic
Translation Groupoids and Orbifold Cohomology
Canadian journal of mathematics, Tome 62 (2010) no. 3, pp. 614-645

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DOI

We show that the bicategory of (representable) orbifolds and good maps is equivalent to the bicategory of orbifold translation groupoids and generalized equivariant maps, giving a mechanism for transferring results from equivariant homotopy theory to the orbifold category. As an application, we use this result to define orbifold versions of a couple of equivariant cohomology theories: $K$ -theory and Bredon cohomology for certain coefficient diagrams.
DOI : 10.4153/CJM-2010-024-1
Mots-clés : 57S15, 55N91, 19L47, 18D05, 18D35, orbifolds, equivariant homotopy theory, translation groupoids, bicategories of fractions 
Pronk, Dorette; Scull, Laura. Translation Groupoids and Orbifold Cohomology. Canadian journal of mathematics, Tome 62 (2010) no. 3, pp. 614-645. doi: 10.4153/CJM-2010-024-1
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     title = {Translation {Groupoids} and {Orbifold} {Cohomology}},
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     year = {2010},
     volume = {62},
     number = {3},
     doi = {10.4153/CJM-2010-024-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-024-1/}
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