In stand mixer bowl combine yeast, warm water and sugar; let stand 10 minutes.
Add oil, salt and 2 cups flour; using paddle attachment, beat until smooth. Mix in enough remaining flour to make dough easy to handle.
Switch to dough hook attachment. Knead until dough is smooth and elastic, about 10 minutes. (NOTE: For hand mixing: following above steps, mix ingredients in large mixing bowl using a wooden spoon or dough whisk. Knead on floured surface until smooth and elastic.)
Place dough in greased bowl. Cover; let rise in warm place until almost double in bulk, about 1 hour.
Punch down dough and turn out on lightly floured surface. Cover and let rest 10 minutes. Divide dough into 16 pieces. Roll out each piece into a 7-inch circle. Cover and let rise 15 minutes.
Meanwhile, preheat oven to 500°F. Place ungreased baking sheet on lowest rack in oven. Quickly transfer a few pitas at a time to heated baking sheet; bake 3 to 4 minutes or until puffed and light brown around the edges. Cool between damp tea towels. Pitas will collapse and soften upon cooling.