  This paper investigates subcycling of particle orbits in variational,
geometric particle-in-cell methods addressing the Vlasov--Maxwell system in
magnetized plasmas. The purpose of subcycling is to allow different time steps
for different particle species and, ideally, time steps longer than the
electron gyroperiod for the global field solves while sampling the local
cyclotron orbits accurately. The considered algorithms retain the
electromagnetic gauge invariance of the discrete action, guaranteeing a local
charge conservation law, while the variational approach provides a bounded
long-time energy behavior.
