Packing subgroups in relatively hyperbolic groups

We introduce the bounded packing property for a subgroup of a countable discrete group G . This property gives a finite upper bound on the number of left cosets of the subgroup that are pairwise close in G . We establish basic properties of bounded packing and give many examples; for instance, every subgroup of a countable, virtually nilpotent group has bounded packing. We explain several natural connections between bounded packing and group actions on CAT.0/ cube complexes.