Can a player be ejected after the final out of the game?

Yes, in major Baseball an umpire can eject a pitcher. Last year as an example, a Yankee pitcher was ejected because the home plate umpire checked to find pine tar on the pitchers belt. This is illegal for a pitcher to have any foreign substance on his body or uniform or cap. Another example is, the umpire's opinion, a pitcher has hit too many batters after being warned. That's an ejection as well. Additionally, any player or manage or a pitcher who argues balls and strikes called by the home plate umpire is an automatic ejection.