We have performed ab initio calculations within the density-functional theory for Ga_1−xMn_xAs diluted semiconductors. Total energy results unambiguously show that a quasi-localized hole, with predominant p-like character, surrounds the fully polarized Mn d⁵-electrons. The calculations indicate that the holes form a relatively dispersionless impurity band, thus rendering effective-mass descriptions of hole states open to challenge. We obtain estimates both for the s = 1/2 hole and S = 5/2 Mn exchange coupling, and for the distance dependence of the effective Mn–Mn exchange interaction. The results demonstrate that the effective Mn–Mn coupling is always ferromagnetic, and thus non-RKKY, and is intermediated by the antiferromagnetic coupling of each Mn spin to the holes.