Definition cfReg (B : {set gT}) : 'CF(B) := #|B|%:R *: '1_[1].

Lemma cfRegE x : @cfReg G x = #|G|%:R *+ (x == 1%g).
Definition xcfun (chi : 'CF(G)) A :=
(gring_row A *m (\col_(i < #|G|) chi (enum_val i))) 0 0.