  This work presents the calculation of the relation between the bare coupling
constant g_0 and the MSbar-renormalized coupling g_MS, g_0 = Z_g(g_0,a\mu)
g_MS, to 2 loops in perturbation theory, with fermions in an arbitrary
representation of the gauge group SU(N). Our calculation is performed using
overlap fermions and Wilson gluons, and the background field technique has been
chosen for convenience. The corresponding results in the fundamental
representation appear in our longer publication [arXiv:0709.4368].
  The 3-loop coefficient of the bare beta-function, b_2^L, is extracted using
the 2-loop expression for Z_g, and it is presented as a function of the overlap
parameter rho, the number of fermion flavors (N_f) and the number of colors
(N). We also provide the expression for the ratio Lambda_L/Lambda_MS, in an
arbitrary representation. A plot of Lambda_L/Lambda_MS is given in the adjoint
representation.
