  Using a new colored analogue of P-partitions, we prove the existence of a
colored Eulerian descent algebra which is a subalgebra of the
Mantaci-Reutenauer algebra. This algebra has a basis consisting of formal sums
of colored permutations with the same number of descents (using
Steingr\'imsson's definition of the descent set of a colored permutation). The
colored Eulerian descent algebra extends familiar Eulerian descent algebras
from the symmetric group algebra and the hyperoctahedral group algebra to
colored permutation group algebras. We also describe a set of orthogonal
idempotents that spans the colored Eulerian descent algebra and includes, as a
special case, the familiar Eulerian idempotents in the group algebra of the
symmetric group.
