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The aim of this paper is to introduce a spectral sequence that converges to the cobordism groups of orbifolds with given isotropy representations. In good cases the E¹-term of this spectral sequence is given by a certain cobordism group of orbibundles over purely ineffective orbifolds which can be identified with the bordism group of the classifying space of the Weyl group of a finite subgroup of O(n). We use this spectral sequence to calculate some cobordism groups of orbifolds for low dimensions,...
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