What is the nature of the narrative ‘Me’?

It is a common experience that memory has a very important role in the configuration of personal identity. The self that I am is a consequence of the one I have been, but above all of what I remember from the one I have been. However, is the self the same as our memory? If memory is altered or lost, can the self remain? If we could transplant somebody’s memory into an inorganic support, would identity be also transplanted?