Geodesic
Computation of the homotopy groups of the set of invertible elements of certain $C^*$-algebras of operators, and applications
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 35 (1980) no. 3, pp. 217-222

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In this paper we compute the homotopy groups of the set of invertible elements of an $n$-fold tensor product of $C^*$-algebras of multi-dimensional Toeplitz operators (§ 1) and construct a representation of the $K^*$-functor with the help of Toeplitz operators (§ 2). 
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     author = {V. M. Deundyak},
     title = {Computation of the homotopy groups of the set of invertible elements of certain $C^*$-algebras of operators, and applications},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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V. M. Deundyak. Computation of the homotopy groups of the set of invertible elements of certain $C^*$-algebras of operators, and applications. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 35 (1980) no. 3, pp. 217-222. http://geodesic.mathdoc.fr/item/RM_1980_35_3_a27/