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