As Virtual Reality (VR) headsets become more mobile, people can interact in public spaces with applications often requiring large arm movements. However, using these open gestures is often uncomfortable and sometimes impossible in confined and public spaces (e.g., commuting in a bus). We present FingerMapper, a mapping technique that maps small and energy-efficient finger motions onto virtual arms so that users have less physical motions while maintaining presence and partially virtual body ownership. FingerMapper works as an alternative function while the environment is not allowed for full arm interaction and enables users to interact inside a small physical, but larger virtual space. We present one example application, FingerSaber that allows the user to perform the large arm swinging movement using FingerMapper.