Add the Greek Seasoning to the meat, toss to combine, and let marinate for at least 15 minutes.
Heat the oil in a large skillet over medium-high heat. When the oil is hot, add the strips of meat and cook until golden brown on all sides. Add the sliced onions and continue to saute until the onions are tender and translucent, about 5-7 minutes. If the mixture is too dry, add a little more olive oil. Add more Greek Seasoning to taste.
Wrap the pitas/flatbreads in aluminum foil and warm them in the oven.
Spread 1/4 cup of the chicken mixture on each pita and top with red cabbage, onions, tomatoes and drizzle with tzatziki sauce. Sprinkle with dried sumac. Serve immediately.