Bhagavad Gita Verse 32, Chapter 13

yathaa sarvagatam saukshmyaadaakaasham nopalipyate |
sarvatraavasthito dehe tathaatmaa nopalipyate || 32 ||
 
Just as all-pervading space, being subtle, is not tainted, so is the self, situated everywhere in any body, not tainted.
 
yathaa : just as
sarvagatam : all pervading
saukshmyaat : being subtle
aakaasham : space
na : not
upalipyate : tainted
sarvatra : everywhere
avasthitaha : situated
dehe : body
tathaa : so
aatmaa : self
na : not
upalipyate : tainted
 
Many scriptures, including the Srimad Bhagavatam, describe the creation of the five great elements. Space was created first, followed by air, fire, water and then earth, each more tangible and visible than the one preceding it. Space, therefore, is the subtlest of elements. Its main property is indivisibility. We may put up walls and differentiate "my room" from "your room", but the wall does not actually divide space at all. The wall is an upaadhi, something that mentally limits space, but cannot ever limit space in reality.
 
Another property of space that it is unaffected by whatever it contains. You can throw dust, water, glue, perfume, odour, anything at all into space, yet it remains unaffected. The air in a room may get affected by perfume or odour, not space. But more fundamentally, space provides existence to everything. Without space, no object can ever exist.
 
Shri Krishna says that the self is similar to space in these aspects. Like space is as though divided into rooms, the self is one but appears as though residing differently in different bodies. Like space never gets tainted by whatever is thrown at it, the self never gets impacted by the results, reactions, experiences and consequences of any action. All actions and reactions stay in the realm of Prakriti. And when we say statements like "this pot is round", we should note that we cannot use the word "is" without realizing that the "is" is the "sat" or existence aspect of the self.
 
How should we bring this teaching into our life? Ultimately, all of us are craving for independence of one form or the other. For instance, the incessant drive to earn more wealth is towards gaining financial independence. Shri Krishna says that once we know that the self in us, the "I" in us is totally unaffected by any reaction or experience of the world, we will gain the highest and utmost level of independence, which is moksha or liberation. We just have to work at removing the ignorance of our true nature, which can only happen if we disassociate from Prakriti and associate with Ishvara.

Bhagavad Gita Verse 15, Chapter 3

karma brahmodbhavam viddhi brahmaaksharasamudhbhavam |
tasmaatsarvagatam brahma nityam yajne pratishthitam || 15 ||
 
Know that actions arise out of the Vedas, and that the Vedas arise out of the imperishable (eternal essence). Therefore, yajna is always established in that all-pervading eternal essence.
 
karma : actions
brahmodbhavam : arise out of the Vedas
viddhi : know
brahma : Vedas
aksharasamudhbhavam : arise out of the imperishable
tasmaat : therefore
sarvagatam : all-pervading
brahma : eternal essence
nityam : always
yajne : yajna
pratishthitam : established
 
Shri Krishna reveals the connection between yajna and the eternal essence in this shloka. Here he says that yajna is an integral part of the eternal essence, because it is born out of the Vedas. Symbolically, the Vedas represent the "rule-book" of the universe, and so yajna becomes an essential law embedded in the universe.
 
In the second chapter, which was an overview of the entire Gita, Shri Krishna pointed Arjuna to the ultimate goal of life - realization of the eternal essence. In this chapter, Shri Krishna connect karmayoga to the eternal essence. He explains that karmayoga is a means, a technique, to realize the eternal essence, because the eternal essence created the rules of the universe.
 
So in summary, the teaching of karmayoga so far is : Actions are of two types,  selfless and selfish. Selfish actions bind us to wordly objects, and selfless actions do not. Therefore, Shri Krishna urges us to move gradually from the level of inaction to selfish action first, and then from selfish action to selfless action or yajna. Only through acting in the spirit of yajna will we move forward on the path to realizing the eternal essence.