When we watch a movie or read a story and identify with a character, we experience the plot through her eyes. We know her: we understand her thoughts, her aspirations; we share her failures and successes; we feel her sorrows and her joys. But we are not her —she is not real; she does not exist in any substantive way.
In the same way, we have developed a character made up of five aggregates (the body and the four mental faculties of sensation, perception, formation, and intention). We have followed this character through every conceivable plot twist. We root for her, and suffer with her, and prolong her existence in our memories.
It is she who accumulates karma. It is she who dies. And it is she who is reborn.