Geodesic
Obstructions to embedding of matrix algebra bundles into a~trivial one
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 3, pp. 27-33.

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Topological obstructions to embedding of an $M_k(\mathbb C)$-bundle into a trivial $M_{kl}(\mathbb C)$-bundle under the condition $(k,l)=1$ are studied. The relation of this problem to the theory of bundles with a structure groupoid is described. 
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A. V. Ershov. Obstructions to embedding of matrix algebra bundles into a~trivial one. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 9 (2009) no. 3, pp. 27-33. http://geodesic.mathdoc.fr/item/ISU_2009_9_3_a4/

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[6] Ershov A. V., Topological obstructions to embedding of a matrix algebra bundle into a trivial one, arXiv: 0807.3544