  Based on the shifted Schensted correspondence and the shifted Knuth
equivalence, a shifted analog of the Poirier-Reutenauer algebra as a higher
lift of Schur's P-functions and a right coideal subalgebra of the
Poirier-Reutenauer algebra is constructed. Its close relations with the peak
subalgebra and the Stembridge algebra of peak functions are also uncovered.
