Chapter IV Sloka 20

Ty®va kmR)las¼< inTyt&Ýae inraïy>,
kmR{yi-àv&Äae=ip nEv ik<icTkraeit s>

tyaktv˜ karmaphal˜saðgaÕ 
nityat®pto nir˜þraya× |
naiva kiñcitkaroti sa× ( 4|20)||

Having abandoned attachment to the fruits of the action, ever content, depending on nothing, he does not do anything though engaged in activity.
The same idea of inaction in action is repeated here to produce a deep impression on the minds of the aspirants. He who works for the well-being of the world and he who performs actions without egoism and attachment to  the fruits of action, to set an example to the masses, really does nothing at all though he is ever engaged in activity, as he possesses the knowledge of the Self which is beyond all activity and as he has realised his identity with It.
As Brahman the Absolute is self-contained, all the desires are gratified if one realises the Self. He is ever satisfied and does not depend on anything, just as a man who has the favour of the king does not depend on the minister or the government official for anything. ( Cf. IV. 41)