Put 3 cups of warm water in a large mixing bowl. Add yeast and sugar. Stir to dissolve. Add 2 cups of all-purpose flour and whisk together. Covered and place the bowl in a warm spot, until the mixture is frothy and bubbling for about 20 minutes.
Add all the remaining flour, salt, olive oil. With a wooden spoon stir until mixture forms a shaggy mass. Knead in the bowl for a few minutes and transfer on your surface and knead lightly for a minute or until smooth.
Clean your bowl coat with olive oil and add the dough back in it. Cover with a towel then places in a warm spot. Leave until dough has doubled in size, it should take about an hour.
Place a pizza stone into your bbq and heat to 450-500 °F. Punch down dough and divide into 12 pieces of equal size. Form each piece into a little ball and put the dough balls on a ate to cover with a towel. Let rise for about 5-10 minutes.
Press the ball into flat disks the roll then into a 6-inch round, as thin as possible.
Lift the dough and put as quick as possible on the very hot stone. After a few minutes, the dough should be nicely puffed like a balloon. Turn over and grill for another minute. Transfer the warm pitas to a basket and cover with a towel so the pitas stay warm and soft. Repeat with all the remaining balls.