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We study the Brauer-Manin obstruction to the Hasse principle and to weakapproximation for 0-cycles on algebraic varieties that possess a fibrationstructure. The exactness of the local-to-global sequence $(E)$ of Chow groupsof 0-cycles was known only for a fibration whose base is either a curve or theprojective space. In the present paper, we prove the exactness of $(E)$ forfibrations whose bases are Ch\^{a}telet surfaces or projective models ofhomogeneous spaces of connected linear algebraic groups with connectedstabilizers. We require that either all fibres are split and most fibressatisfy weak approximation for 0-cycles, or the generic fibre has a 0-cycle ofdegree $1$ and $(E)$ is exact for most fibres.

Local-global principle for 0-cycles on fibrations over rationally connected bases