Geodesic
$K$-theory on the category of infinite cell complexes
Izvestiya. Mathematics , Tome 2 (1968) no. 3, pp. 515-556

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The main purpose of the article is to compute cohomology operations in $K$-theory $\operatorname{mod}p$ and operations from the usual cohomology theory into $K$-theory. The proposed method is based on the extension of $K$-theory to a category of infinite complexes, which makes it possible to use spectral sequences of the “bar-construction” type. 
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     author = {V. M. Buchstaber and A. S. Mishchenko},
     title = {$K$-theory on the category of infinite cell complexes},
     journal = {Izvestiya. Mathematics },
     pages = {515--556},
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     volume = {2},
     number = {3},
     year = {1968},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1968_2_3_a2/}
}
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V. M. Buchstaber; A. S. Mishchenko. $K$-theory on the category of infinite cell complexes. Izvestiya. Mathematics , Tome 2 (1968) no. 3, pp. 515-556. http://geodesic.mathdoc.fr/item/IM2_1968_2_3_a2/