Put the chicken breasts in a 5-quart slow cooker and sprinkle them with the cumin and salt.
Pour the salsa verde over the chicken, cover and cook on low until the thickest piece reaches 165°F, 3 1/2 to 4 hours.
Move the chicken to a shallow bowl and shred it into thick strands with two forks.
Skim excess fat from the cooker, return the chicken and fold it through the salsa.
Cover on warm for 10 minutes while you heat the corn tortillas in a dry skillet.
Fill each tortilla with chicken, cabbage and cotija and serve with lime wedges.