  We identify two seemingly disparate structures: supercharacters, a useful way
of doing Fourier analysis on the group of unipotent uppertriangular matrices
with coefficients in a finite field, and the ring of symmetric functions in
noncommuting variables. Each is a Hopf algebra and the two are isomorphic as
such. This allows developments in each to be transferred. The identification
suggests a rich class of examples for the emerging field of combinatorial Hopf
algebras.
