To make the chicken, combine the olive oil and next 12 ingredients (through lime juice) in a ziplock bag; massage bag to mix well and add chicken. Turn to coat and refrigerate for 4 hours, or overnight. Allow chicken to sit at room temperature for 15-30 minutes before cooking.
To make the salsa, preheat grill to 400 degrees F and grill pineapple, bell pepper, onion, and jalapeno until charred, about 4-5 minutes per side. Remove from grill and allow to cool slightly. Dice the grilled ingredients and combine in a medium bowl with the cilantro, ginger, cumin, salt, and pepper; toss well and refrigerate until ready to serve.
To cook the chicken, grill for 6-8 minutes per side or cook in a nonstick skillet over medium heat for 10-12 minutes, turning once, or until cooked through. Remove chicken to a cutting board; allow to rest for 5 minutes before slicing.
Meanwhile, combine the avocado crema ingredients in a mini food processor or blender and pulse until nearly smooth; set aside.
To assemble, layer ~3.5 ounces of chicken in each tortilla and top with salsa and avocado crema. Serve immediately.