Geodesic
The $K$-functOr (Grothndieck group) of the infinite symmetric group.
Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part V, Tome 123 (1983), pp. 126-151

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The Grothendieck group $K_0(\sigma_\infty)$ of the group $\sigma_\infty$ of finite permutations of a countable set is described. We also discribe all semifinite characters of this group and use them to determine the cone of true $K_+^0(\sigma_\infty)$ representations. 
@article{ZNSL_1983_123_a9,
     author = {A. M. Vershik and S. V. Kerov},
     title = {The $K${-functOr} {(Grothndieck} group) of the infinite symmetric group.},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {126--151},
     publisher = {mathdoc},
     volume = {123},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1983_123_a9/}
}
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A. M. Vershik; S. V. Kerov. The $K$-functOr (Grothndieck group) of the infinite symmetric group.. Zapiski Nauchnykh Seminarov POMI, Differential geometry, Lie groups and mechanics. Part V, Tome 123 (1983), pp. 126-151. http://geodesic.mathdoc.fr/item/ZNSL_1983_123_a9/