Preheat an indoor or outdoor grill to high.
In a bowl, combine the coriander, cumin, cardamom, chili powder, paprika and grill seasoning. And the juice of half a lemon, the garlic and about 3 tablespoons olive oil and stir until it is paste-like.
Slather the mixture all over the chicken until it is well-coated.
Transfer to the grill and cook on each side for 6-7 minutes, until cooked through.
Remove from the grill and let the chicken rest before thinly slicing.
Once the chicken is working, preheat a large skillet over medium-high heat with 2 turns of the pan of olive oil, about 2 tablespoons. Once you see the oil ripple, add the onions and peppers, and season with some salt and pepper.
Cook, stirring frequently, for about 5 minutes until the veggies start to wilt. Once the onions are working make the sauce: In a bowl, combine the juice of the remaining half lemon, the tahini, yogurt, some salt and a small drizzle of olive oil. Mix to combine.
Place the pitas on the grill to warm them and give them a light char, about 1 minute on each side. To assemble, place some of the sliced chicken on each pita, top with some of the pepper and onion mixture, and a good dollop of the yogurt-tahini sauce.