Geodesic
On the zeroth stable $\mathbb A^1$-homotopy group of a~smooth projective variety
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 5-8

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The zeroth stable $\mathbb A^1$-homotopy group of a smooth projective variety is computed. This group is identified with the group of oriented zero-cycles on the variety. The proof heavily exploits properties of strictly homotopy invariant sheaves. 
@article{ZNSL_2016_443_a0,
     author = {A. S. Ananyevskiy},
     title = {On the zeroth stable $\mathbb A^1$-homotopy group of a~smooth projective variety},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--8},
     publisher = {mathdoc},
     volume = {443},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_443_a0/}
}
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A. S. Ananyevskiy. On the zeroth stable $\mathbb A^1$-homotopy group of a~smooth projective variety. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 5-8. http://geodesic.mathdoc.fr/item/ZNSL_2016_443_a0/