Having abandoned attachment to the fruits of actions, ever content, depending on nothing, he does not do anything though engaged in activity. The Gita seems to emphasize Karma Yoga, for Arjuna is persuaded to fight. Sri Krishna himself set the example by an active life of great exploits. Actions will go on even in the egoless state. Each person has come into manifestation for a certain purpose and that purpose will be accomplished whether he considers himself to be the actor or not.
All actions go on automatically.
It is said in all the scriptures that you should not consider yourself to be the actor. The Gita teaches that one should have an active life from beginning to end. Analyzing them and enquiring into their truth, one is obliged to remain as the Self in peace. Nevertheless even in that state the actions will go on. No, not the Self.