  We consider global monopoles as well as black holes with global monopole hair
in Einstein-Goldstone model with a cosmological constant in four spacetime
dimensions. Similar to the $\Lambda=0$ case, the mass of these solutions
defined in the standard way diverges. We use a boundary counterterm subtraction
method to compute the mass and action of $\Lambda \neq 0$ configurations. The
mass of the asymptotically de Sitter solutions computed in this way turns out
to take positive values in a specific parameter range and, for a relaxed set of
asymptotic boundary conditions, yields a counterexample to the maximal mass
conjecture.
