In a small saucepan, whisk together 1/2 cup (125 ml) of the water and the cornstarch. Bring to a boil, whisking constantly until the mixture forms a firm paste. Transfer to a bowl, cover with plastic wrap and let cool.
In a small bowl, combine the remaining water and the yeast. Let rest for 5 minutes.
In a food processor, combine the flour, sugar, salt and oil with the cooled starch and yeast mixtures. Process until smooth. Place the dough in a lightly oiled bowl, turning to coat with the oil. Cover with plastic wrap and let rest in a warm place for 2 hours.
Divide the dough into 8 equal pieces. On a surface lightly floured with gluten-free flour, using a rolling pin, roll out each piece of dough into a 6-inch (15 cm) disc.
Heat a lightly oiled, non-stick skillet over medium heat. When the skillet is hot, cook one disc at a time for 2 minutes. Flip and continue cooking for 1 minute or until lightly browned. Set aside on a wire rack. Wipe the skillet clean with a lightly oiled paper towel before cooking each pita.