  Kite pseudo effect algebras were recently introduced as a class of
interesting examples of pseudo effect algebras using a po-group, an index set
and two bijections on the index set. We represent kite pseudo effect algebras
with a special kind of the Riesz decomposition property as an interval in a
lexicographic extension of the po-group which solves an open problem on
representation of kites. In addition, we introduce kite $n$-perfect pseudo
effect algebras and we characterize subdirectly irreducible algebras which are
building stones of the theory.
