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This is joint work with Cristina Costoya. We construct a model structure in the category of orbifold groupoids and prove that its homotopy category is the category of orbifolds introduced by Moerdijk. To each orbifold groupoid we can associate a category fibered in groupoids (CFG) which is not necessarily a stack. We will say that an orbifold groupoid is a stack groupoid if the associated CFG is a stack. The fibrant objects of our model are the stack groupoids.