  We report a study of multi-muon events produced at the Fermilab Tevatron
collider and recorded by the CDFII detector. In a data set acquired with a
dedicated dimuon trigger and corresponding to an integrated luminosity of 2100
pb^-1, we isolate a significant sample of events in which at least one of the
muon candidates is produced outside of the beam pipe of radius 1.5cm. The
production cross section and kinematics of events in which both muon candidates
are produced inside the beam pipe are successfully modeled by known QCD
processes which include heavy flavor production. In contrast, we are presently
unable to fully account for the number and properties of the remaining events,
in which at least one muon candidate is produced outside of the beam pipe, in
terms of the same understanding of the CDFII detector, trigger, and event
reconstruction. Several topological and kinematic properties of these events
are presented in this paper. These events offer a plausible resolution to
long-standing inconsistencies related to b-bbar production and decay.
