  We construct unital extensions of the higher order peak algebras defined by
Krob and the third author in [Ann. Comb. 9 (2005), 411--430.], and show that
they can be obtained as homomorphic images of certain subalgebras of the
Mantaci-Reutenauer algebras of type B. This generalizes a result of Bergeron,
Nyman and the first author [Trans. AMS 356 (2004), 2781--2824.].
