  G-Brownian motion has a very rich and interesting new structure which
nontrivially generalizes the classical one. Its quadratic variation process is
also a continuous process with independent and stationary increments. We prove
a self-normalized functional central limit theorem for independent and
identically distributed random variables under the sub-linear expectation with
the limit process being a G-Browian motion self-normalized by its quadratic
variation. To prove the self-normalized central limit theorem, we also
establish a new Donsker's invariance principle.
