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ALGEBRAIC AND GEOMETRIC TOPOLOGY, vol.12, no.3, pp.1313-1330, 2012 (SCI-Expanded)
Let G be a finite group and H be a family of subgroups of G which is closed under conjugation and taking subgroups. Let B be a G-CW-complex whose isotropy subgroups are in H and let F = {F-H}(H is an element of H) be a compatible family of H-spaces. A G-fibration over B with the fiber type F = {F-H}(H is an element of H) is a G-equivariant fibration p: E -> B where p(-1)(b) is G(b)-homotopy equivalent to F-Gb for each b is an element of B. In this paper, we develop an obstruction theory for constructing G-fibrations with the fiber type F over a given G-CW-complex B. Constructing G-fibrations with a prescribed fiber type F is an important step in the construction of free G-actions on finite CW-complexes which are homotopy equivalent to a product of spheres.