  The spin analogues of several classical concepts and results for Hecke
algebras are established. A Frobenius type formula is obtained for irreducible
characters of the Hecke-Clifford algebra. A precise characterization of the
trace functions allows us to define the character table for the algebra. The
algebra is endowed with a canonical symmetrizing trace form, with respect to
which the spin generic degrees are formulated and shown to coincide with the
spin fake degrees. We further provide a characterization of the trace functions
and the symmetrizing trace form on the spin Hecke algebra which is Morita
super-equivalent to the Hecke-Clifford algebra.
