This is a tough one, since projections introduce distortion when going from the 3D WGS84 geographic coordinate system to a flat 2D projection. At a global scale, you're bound to have distortions somewhere in the system.
I think your best bet is to project to the Universal Transverse Mercator projection. As far as I know this is the closest you can get to a global projection with the least amount of distortion.
If you can relax the requirementrequirements that groups have to be defined in areas of the exact same size as well as the requirement of real-time processing, there are clustering algorithms such as DBSCAN, and a family of derivatives, that can help produce these groupings.