Frobenius morphisms and derived categories on two dimensional toric Deligne-Mumford stacks

For a toric Deligne-Mumford (DM) stack X, we can consider a certain generalization of the Frobenius endomorphism. For such an endomorphism F:X→X on a 2-dimensional toric DM stack X, we show that the push-forward F∗OX of the structure sheaf generates the bounded derived category of coherent sheaves on X.We also choose a full strong exceptional collection from the set of direct summands of F∗OX in several examples of two dimensional toric DM orbifolds X.