How does sun heat the air?

Is is a great question, and one I am currently working with. Our understanding of the atmosphere, I think, is incomplete, and needs reviewed and updating. Doing so will easily explain such a problem. As it stands there are deep contradictions and paradoxes associated with radiation and the atmosphere.
Air is a near perfect insulator (it has a conduction value of near zero; 0.024 no units) so the thought heat energy is transferred this way cannot be so .
Add to that: air is assumed to (with the exception of about 1% greenhouse gases) not absorb or emit any IR radiation: this is a contradiction to Radiation theory, and quantum mechanics where all matter above absolute 0 Kelvin radiates IR.

So something is wrong, because the air does increase, and decrease in temperature, and does so quickly.
My hypothesis is O2 and N2 (99% of the dry atmosphere) do absorb and emit IR radiation: I have the quantum theory to show where they do, the experimental instrument to show it does, and the application proof to show it does.

I am currently writing up my work - it is a massive undertaking; I predict the biggest upset is science of our time: greenhouse theory will collapse. Special greenhouse atmosphere theory is pre quantum mechanics 19th Century science; it has not been updated with 20th Century knowledge - yet.