We consider modular representations of a finite group and focus for each prime ideal of the cohomology ring on the stable category of representations supported at that prime. This category is tensor triangulated, but compact and dualising objects do not coincide. For instance, the tensor unit is not compact. This is in contrast to the global category of representations and leads to an interesting completion of the category of compact objects. The talk presents recent progress from an ongoing collaboration with Dave Benson, Srikanth Iyengar, and Julia Pevtsova.