  We make use of the global symmetries of the Yang-Mills theory on the lattice
to design a new computational strategy for extracting glueball masses and
matrix elements which achieves an exponential reduction of the statistical
error with respect to standard techniques. By generalizing our previous work on
the parity symmetry, the partition function of the theory is decomposed into a
sum of path integrals each giving the contribution from multiplets of states
with fixed quantum numbers associated to parity, charge conjugation,
translations, rotations and central conjugations Z_N^3. Ratios of path
integrals and correlation functions can then be computed with a multi-level
Monte Carlo integration scheme whose numerical cost, at a fixed statistical
precision and at asymptotically large times, increases power-like with the time
extent of the lattice. The strategy is implemented for the SU(3) Yang--Mills
theory, and a full-fledged computation of the mass and multiplicity of the
lightest glueball with vacuum quantum numbers is carried out at a lattice
spacing of 0.17 fm.
