Geodesic
Grothendieck group for the stable category
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 12, Tome 321 (2005), pp. 5-12

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In this paper we describe Cartan matrices of symmetric special biserial algebras and compute the order of Grothendieck group for the stable category of these algebras. In particular, we obtain a criterion for existence of a free summand in these groups. 
@article{ZNSL_2005_321_a0,
     author = {M. A. Antipov},
     title = {Grothendieck group for the stable category},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--12},
     publisher = {mathdoc},
     volume = {321},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_321_a0/}
}
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M. A. Antipov. Grothendieck group for the stable category. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 12, Tome 321 (2005), pp. 5-12. http://geodesic.mathdoc.fr/item/ZNSL_2005_321_a0/