  We study the quantum contributions to the classical cosmological constant in
a quantum gravity theory for GR with matter on a piecewise linear spacetime
corresponding to a triangulation of a smooth manifold. We use the effective
action approach and a special path-integral (PI) measure which depends on a
free parameter, while matter is modeled by a massive self-interacting scalar
field. The effective cosmological constant (CC) is given as a sum of 3 terms:
the classical CC, the quantum gravity CC and the matter CC. We show that the
free parameters of the theory can be chosen such that the classical CC cancels
the matter CC so that the effective CC is given by the QG CC. Since the value
of the quantum gravity CC is determined by the PI measure only, the PI measure
parameter can be chosen such that the effective CC gives the observed value.
This is equivalent to the statement that the experimentally observed CC value
belongs to the spectrum of the CC operator in this QG theory.
