Bulletin of the
Korean Mathematical Society BKMS

Let $F^\alpha G$ be a twisted group algebra with basis $\{u_g |g
\in G\}$ and ${\mathcal P}= \{ {\mathcal C}_g | g \in G \}$ be a
partition of $G$. A projective class algebra associated with
${\mathcal P}$ is a subalgebra of $F^\alpha G$ generated by all
class sums $\sum_{x \in {\mathcal C}_g} u_x$. 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 $\alpha$-spherical function will play an important role for the
purpose. We find functional properties of $\alpha$-spherical
functions and investigate roles of $\alpha$-spherical functions as
characters of projective class algebras.

Keywords: spherical functions, group characters

MSC numbers: 16H05, 16P99