The coupling of optical and electronic degrees of freedom together with quantum confinement in low-dimensional electron systems is particularly interesting for achieving exotic functionalities in strongly correlated oxide electronics. Recently, high room-temperature mobility has been achieved for a large bandgap transparent oxide - BaSnO$_3$ upon extrinsic La or Sb doping, which has excited significant research attention. In this work, we report the observation of room-temperature ferromagnetism in BaSnO$_3$ thin films and the realization of a two-dimensional electron gas (2DEG) on the surface of transparent BaSnO$_3$ via oxygen vacancy creation, which exhibits a high carrier density of $sim 7.72*10^{14} /{rm cm}^2$ and a high room-temperature mobility of ~18 cm$^2$/V/s. Such a 2DEG is rather sensitive to strain and a less than 0.1% in-plane biaxial compressive strain leads to a giant resistance enhancement of 350% (more than 540 kOhm/Square) at room temperature. Thus, this work creates a new path to exploring the physics of low-dimensional oxide electronics and devices applicable at room temperature.
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