Combine 2 cups flour, corn meal and salt. Cut in 1/3 cup margarine and shortening until mixture resembles coarse crumbs. Stir in cheese. Add water, 1 tablespoon at a time, stirring lightly until mixture forms a ball. Divide dough into 2 parts, 1 slightly larger; shape each to form ball. Wrap securely in plastic wrap or wax paper; chill about 30 minutes. Roll large ball on lightly floured surface to form 11-inch circle. Fit loosely into 9-inch pie plate; trim. Roll remaining dough to form 12-inch square. Cut into 12 x 3/4-inch strips.

Heat oven to 400 F. Combine remaining 1/3 cup flour, apples, sugar and cinnamon; spoon into crust. Dot with remaining 2 tablespoons margarine. Weave strips atop filling to make a lattice crust. Trim even with outer rim of pie plate. Fold lower crust over strips; seal and flute. Bake 30 to 35 minutes or until crust is light golden brown, shielding edges with aluminum foil if necessary. Cool slightly.