== is there an isotropy subgroup for a properly discontinuous action? == 

 The article on Orbifold says: The main example of underlying space is a quotient space of a manifold under the properly discontinuous action of a possibly infinite group of diffeomorphisms with finite isotropy subgroups. In particular this applies to any action of a finite group; 

 I want to agree. But I'm confused. If the action of the group were free + properly discontinuous, we'd get a manifold as a quotient, wouldn't we? But how does this make sense? How can a properly discontinuous action be non free? If there is a point that is fixed by some group element, we'll always have that group element in the set . How can that be the case?  

 And why is freely discontinuous a redirect to this article? What does freely discontinuous mean? 

 This is probably terrible obvious, but I don't see it right now. Maybe tomorrow.