  We extend to several combinatorial Hopf algebras the endomorphism of
symmetric functions sending the first power-sum to zero and leaving the other
ones invariant. As a transformation of alphabets, this is the (1-E)-transform,
where E is the exponential alphabet, whose elementary symmetric functions are
e_n=1/n!. In the case of noncommutative symmetric functions, we recover
Schocker's idempotents for derangement numbers [Discr. Math. 269 (2003), 239].
  From these idempotents, we construct subalgebras of the descent algebras
analogous to the peak algebras and study their representation theory. The case
of WQSym leads to similar subalgebras of the Solomon-Tits algebras. In FQSym,
the study of the transformation boils down to a simple solution of the Tsetlin
library in the uniform case.
