Periodic resolutions and finite group actions

In this thesis, non-free actions of a finite group with a given family of isotropy subgroups are considered. An algebraic setting is established to study these actions. It is proved that if a finite group has periodic cohomology of period n with respect to a given family, then there exists a periodic relative projective resolution of length n. The modules over the orbit category for a given finite group and family are also considered and it is shown that certain type of resolutions over the orbit category are geometrically realizable.