Suppose $G$ is a finite group and $F$ is a field. Is $F[G\wr S\_n]$ a cellular algebra ?. If so, what is a cellular basis for that algebra.



Is $F[G\wr S_n]$  a cellular  algebra ?
I don't believe that $F[G]$ is cellular in general. My reason (and this is not a proof) is that cellular algebras are typically quasi-hereditary (which implies finite cohomological dimension) and group algebras are not close to quasi-hereditary.


