If I am not the skandhas, then what entity/group of entities am I being responsible for by being a good person? I'm look more for an epistemological Buddhist answer to this question.

If I am anatta (not self because composite) then who is the one responsible for his/her actions? Why am I still responsible for my karma? What is it that transmutes from life to life?
Who is the one making the choice?
Why is it even possible to do good (as opposed to fatalistically going along with things)?

How do you resolve this paradoxical quandary?

Edit:
To clarify the cause of my question, it was not mere metaphysical musings. I want to know more about the Director, the Leader, the Chooser because not only is it more conducive to proper behavior but actually because I want to more practically cultivate the specific aspect of Buddhism which indicates that we can direct our rebirths to a very high degree after death.
The answer to this question I believe is Awareness as Tibetan Buddhism would indicate where it is repetatively emphasized that we should cultivate so as to be aware throughout the death process and not startled by the manifestations. Thus, we can choose and direct our rebirth with clear functioning.
Buddhist concept of not self is always difficult to translate. It generally means:


There is no core or soul
You have no absolute control over your aggregates or the world at large


Also when you have the perception of self you have a yard stick which you use to measure other people, their actions, standing, wealth, etc. with respect to you. This creates misery. If you drop the yard stick then you get out of misery.

Having said this though there is no lasting entity as you there is a mind matter process. What ever you do becomes fabrications which at that point influence the process and also has a "loop back" at different times.