Arrange chicken in slow cooker stoneware. Sprinkle with salt and pepper.
In a small bowl, combine garlic, ginger, soy sauce, sesame oil and 1/4 cup water. Pour over chicken.
Cover and cook on Low for 6 to 7 hours or on High for 3 to 3 1/2 hours, until juices run clear when chicken is pierced with a fork. Using a slotted spoon, transfer chicken to a cutting board. Using two forks, shred meat. Return meat to sauce in stoneware.
Preheat oven to 350°F (180°C). Stack tortillas and wrap them in foil. Warm in oven for 10 minutes.
Spread 1 tbsp hoisin sauce over each tortilla, then top with one-quarter of the chicken mixture, 1/4 cup of the broccoli slaw and red pepper. Fold or roll up tortillas.
Notes
There is no need to peel ginger root before grating it. Simply scrub it and use a standard box grater with fine holes. You can wrap any unused ginger root in plastic wrap and freeze it for up to 6 months, then grate the frozen ginger root as you need it.