Fact linear_char_key B : pred_key (@linear_char B). Proof. by []. Qed.
Canonical linear_char_keted B := KeyedQualifier (linear_char_key B).
Fact linear_char_divr : divr_closed (@linear_char G).
Canonical lin_char_mulrPred := MulrPred linear_char_divr.
Canonical lin_char_divrPred := DivrPred linear_char_divr.

Lemma irr_inv i x : 'chi[G]_i x^-1%g = ('chi_i x)^*.