Action as per Lord Krishna in Bhagavad Gita directly relates to karma but inherent karma is much more than mere physical action. As per Bhagavad Gita, primarily Jaina philosophy every single thought precipitates into an act of karma.
When we invoked a thought, no physical action took place yet, invoking of thoughts precipitate into karma. And what does this mean? Philosophically, spiritually this means in the cosmic game of life even if we idle, karma continues its cycle within us in form of thoughts.
Karma in Bhagavad Gita not only relates to physical action but also mental action.
During Kurukshetra battle around 3600 years before there were no nuclear armament yet Sudarshan chakra, Brahmastra etc. seemed like weapons of mass destruction. The main philosophy behind usage of such armament was mental power. All such destructive weapons could be used only by one with a highly evolved mental power.
As per Bhagavad Gita both physical and mental actions were equally important and played vital role.
Furthermore, the whole philosophy of Bhagavad Gita is based on nishkama karma yoga, offering fruits of all actions to God Almighty all the time. As per Gita mankind was duty bound to indulge in karma (action, both physical and mental) but the fruits of those actions never belonged to the individual self, it always belonged to our true inner self existing in heart as soul atman.
In nutshell, Lord Krishna in Bhagavad Gita says we are primarily a spiritual being manifesting human form. The physical action indulged by the manifest physical body, all results thereof belonged to the spiritual being within. A highly evolved spiritual person can easily understand this analogy but for commoners, masses it was slightly difficult to understand.
Spiritually all fruits of karma indulged by manifest physical body belonged to us but understanding it in physical life is difficult. For this we need to realize that we are primarily a spirit, a consciousness manifesting a form. As per Bhagavad Gita we are always a trustee, caretaker in the journey of life. The fruits of all action indulged always belonged to the rightful owner, our soul atman. It is only due to presence of ego we failed to understand this analogy.
As per Bhagavad Gita the physical manifest human body was only a means to an end. The physical body is manifested by soul atman to cleanse self of dross impurities within. For the manifest physical body to indulge in action, karma God Almighty ordained presence of ego. In absence of ego no living being on mother earth including human beings would ever indulge in action. But spirituality was all about demolishing our ego in totality and reaching our true inner self.
In the battle of Mahabharata when Arjuna refused point blank to indulge in action even when facing the enemy Lord Krishna imparted sermon of Bhagavad Gita to Arjuna for him to realize his Dharma and provoke him for indulging in action, karma. As an enlightened one when Arjuna truly realized his inner being, he prepared himself to fight the enemy head-on.
Until the time Arjuna realized he was a soul atman, he feigned cowardice. This happened because Arjuna was treating himself as an individual. After reaching state of enlightenment when Arjuna thought about outcome of war if he practiced cowardice, he realized that he was only a pawn, a medium and indulging in karma action was not for him to decide.
As a spiritual traveler, indulging in war was his Dharma, prime reason why the sermon by Lord Krishna, Dharmaraja himself got necessitated.
Realizing that Lord Krishna represented God Almighty on mother earth and Arjuna represented his countrymen and soldiers, Arjuna finally picked arms to fight the enemy.
If a spiritual traveler thinks indulging in action karma was not one’s job, we are mistaken. Karma could never be burnt that way. To annihilate karma in totality our indulgence in karma is necessitated. Arjuna finally realized folly of his premature thinking.
About action Lord Krishna in Bhagavad Gita simply says not to attach self to fruits of karma performed. We have to indulge; we have to do our part of karma but with an unattached attitude, similar as indulged by JRD Tata and also King Janaka (father of Sita in Ramayana). Both these stalwarts of their fields always indulged in action, karma with an unattached attitude.
Detachment, working with an unattached attitude was never about running away from action, karma. A spiritual traveler always indulges in karma not for the sake of karma but the ultimate underlying results. An action that does not produce attachment is what nishkama karma all about.
Furthermore, action karma by Arjuna in the battle of Mahabharata was directed more towards re-establishing of Dharma (righteousness) than merely winning a war. When society reaches its lowest ebb, a point of no return then a war like Mahabharata gets necessitated to uproot evil. So that Arjuna succeeds re-establishing Dharma, the sermon of Bhagavad Gita was delivered by Lord Krishna.