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Let k be a field, G a smooth connected linear algebraic group and X ahomogeneous space of G over k, such that the geometric stabilizers areextensions of a smooth group of multiplicative type by a smooth connectedcharacterfree group. If k has characteristic zero and if X^c is a smoothcompactification of X over k, we obtain a formula for the algebraic Brauergroup of X^c. Several variants are obtained in positive characteristic p,including the finite field case and the global field case, where the formulaedescribe the prime-to-p part of the algebraic unramified Brauer group of X,without assuming the existence of a smooth compactification of X. Moreover,assuming that stabilizers are connected, then our formulae hold for theprime-to-p part of the whole unramified Brauer group.

Complexes de groupes de type multiplicatif et groupe de Brauer non ramifi\'e des espaces homog\`enes