  Quantum antiferromagnets on geometrically frustrated lattices often allow a
number of unusual paramagnetic ground states. The fate of these Mott insulators
upon doping is an important issue that may shed some light on the high $T_c$
cuprate problem. We consider the doped Mott insulator on the Shastry-Sutherland
lattice via the t-J model. The U(1) slave-boson mean field theory reveals the
strong competition between different broken symmetry states. It is found that,
in some ranges of doping, there exist superconducting phases with or without
coexisting translational-symmetry- breaking orders such as the staggered flux
or dimerization. Our results will be directly relevant to SrCu$_2$(BO$_3$)$_2$
when this material is doped in future.
