While Caesar is certainly not the main player on the stage of Shakespeare's Julius Caesar (he is, after all, dead by the middle of the third Act), it's still possible to argue that his spirit, or rather his character, continues to influence the entire course of the play.
This idea might surprise some readers. After all, it's pretty easy to see that the main plot of Shakespeare's play is more concerned with the tragic figure of Brutus and his fellow conspirators than with the eponymous emperor. Be that as it may, it's important to recognize that, if it weren't for Caesar's arrogant ambition to rule all of Rome, none of the events of the play would have ever taken place. As such, though Caesar himself does not play a major role in most of the events in Julius Caesar, his character is responsible for the drama that unfolds: his ambition to become emperor leads the conspirators to assassinate him, which in turns leads to a bloody civil war. As such, it would be very accurate to claim that the spirit of Caesar influences the entire course of the play.