In Buddhist doctrine there is always the problem, that for the sake of understandability, certain concepts are being presented in a solid, substantial way, while actually, one has to keep in the back of one's mind, that by the central tenet of anattā/anātman these concepts are actually not like that. The same applies to kamma/karma, which can be presented as something that a being accumulates and carries with itself in this life and to the next and the ones following.
Now, actually, there is nothing substantial that transmigrates from one life to the next, as is clear from the similes that are used to explain rebirth without soul: a candle that lights another, an echo, a mirror image, the imprint in wax of seal. In these cases, though there is some link between the two sides, nothing actually goes from one to the other (the case with the echo should maybe be reconsidered according to the old Indian theories of sound and the echo). So, what is kamma/karma? How does it stick to the individual?
To take this question one step further, if we admit now that kamma/karma is near-identical with the concept of saṃskāra/saṃkhāra, and therefore with volitions and cetanā, as in this quote from AN 6.63:
cetanāhaṃ bhikkave kammaṃ vadāmi
Intention, I tell you, is kamma
and that by karmic unwholesome action the consciousness "leans towards" unwholesomeness, then how are these leanings supposed to look, how are they thought to be transported from one conscious moment to the next?