Place the chicken breasts in the slow cooker. Add 16 ounces of the salsa verde along with the cumin, garlic powder, and salt.
Cover and cook on low for 6 hours, until the chicken shreds easily with a fork.
Shred the chicken directly in the slow cooker and stir it into the remaining sauce.
Heat the oven to 375 degrees. Warm the tortillas briefly so they stay flexible.
Spoon chicken into each tortilla, add a little cheese, roll them up, and place them seam side down in a baking dish.
Pour the remaining 4 ounces of salsa verde over the top and sprinkle with the rest of the cheese.
Bake for 15 minutes, until the cheese melts. Finish with cilantro and serve lime wedges on the side.