Let $F^{alpha}G$ be a twisted group algebra with basis ${{mu}g|g;{in};G}$ and $P;=;{C_g|g;{in};G}$ be a partition of G. A projective class algebra associated with P is a subalgebra of $F^{alpha}G$ generated by all class sums $sumlimits{_{x{in}C_g}};{mu}_x$. A main object of the paper is to find interrelationships of projective class algebras in $F^{alpha}G$ and in $F^{alpha}H$ for H < G. And the a-spherical function will play an important role for the purpose. We find functional properties of a-spherical functions and investigate roles of $alpha-spherical$ functions as characters of projective class algebras.