Yes, the theory of Karma (the original Hindu idea, not the westernized appropriated version) rests on the premise of the existence of the eternal Atman, or the Self, where actions produce Sanskara (Imprints, impressions) on the Atman.
Some quotes from Yoga Sutra may help.
CHAPTER IV – KAIVALYA PADA
INDEPENDENCE
tadasankhyeyavasanachitram api pararthan
sanhatyakaritvat
23) The mind through its innumerable desires acts for
another (the Purusa), being combinations.
(the mind is the instrument to conduct actions for the Purusha (Atma).
As for Karma
karmashuklakrishnnam yoginah trividham itaresham
7) Karma are neither black nor white for the Yogis; for
others they are threefold, black, white, and mixed.
(Here Black and White can be taken to mean Good and Bad)
tatastadvipakanugunanam evabhivyaktirvasananam
8) From these threefold works are manifested in each
state only those desires (which are) fitting to that state
alone. (The others are held in abeyance for the time
being.)
Desires express themselves in the right environment, then actions (Karma) are performed according the desires and reaction (Karma) occurs according to the environment.
Karma is the means to attain perfection, and in Yoga Sutras of Patanjali we find such sutras as.
prasankhyanepyakusidasy sarvathavivekakhyater
dharmameghah samadhih
28) Even when arriving at the right discriminating
knowledge of the senses, he who gives up the fruits,
unto him comes as the result of perfect
discrimination, the Samadhi called the Dharma Megha (Cloud of Dharma)
tatah kleshakarmanivrittih
29) From that comes cessation of pains and Karma.
Here the fruits of ones actions are to be given up to attain freedom from all Karma (reaction). Actions will always be performed and reactions will always be there but if attachment to the results be removed, the pains of the reacting Karma are lessened, how to remove them, well that is the entire point of Yoga.