In a mixing bowl, combine the flour, baking powder, and salt. Cut in the shortening until the mixture resembles the consistency of cornmeal. Gradually blend in 2/3 cup water. Knead the dough on a clean surface for 5 minutes, or until smooth. Divide the dough into 3 equal parts. Roll out each portion of dough into a 1/8-inch thick circle. Using a pastry wheel, cut each circle into quarters. While the dough is resting, heat the oil in a deep heavy pot until it reaches 350°. Working in batches, fry the sopaipillas, turning with a slotted spoon, for 2 to 3 minutes, or until a pale golden color. Drain on paper towels and serve hot.