If you do not experience moral obligation, does that imply that nothing you do is right or wrong according to Kant?
Kant believes unequivocally in an objective right and wrong. The standard that he applies to action in deciding whether it is right or wrong is called the "categorical imperative," and comes in three forms. The first formulation involves the standard of universalizability, and asks whether you could will that the proposed course of action become a universal law. That is to ask ourselves, "In the kind of situation that I am in, would it be a good thing if everyone did what I'm about to do?"
The second formulation of the categorical imperative requires treating others as ends in themselves and not as means only, and the third formulation involves promotion of a "kingdom of ends," which is for Kant a kind of social ideal in which every rational being lives by common objective laws that include mutual respect.
All decisions are regulated by either categorical or hypothetical imperatives. Hypothetical imperatives are those which govern prudent action, or action that is beneficial given a particular goal. (I want to do well in my philosophy class, therefore I must read the assigned literature.) Decisions that are governed by categorical imperatives have objectively right and wrong courses of action.
Kant says that our decisions should be governed by a sense of duty to uphold the moral law. However, making the morally correct decisions in spite of not feeling that sense of moral obligation helps to cultivate a virtuous volition. In fact, Kant indicates that the only thing that is truly good without qualification is a good will. He also claims that it is the intent of the person acting that makes the action truly good, not the effect of the action. Thus in Kant's eyes, even if your good action turns out badly, it is still good because of your good will in acting.