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In this article we build a Quillen model category structure on the categoryof sequentially complete l.m.c.-C*-algebras such that the correspondinghomotopy classes of maps Ho(A,B) for separable C*-algebras A and B coincidewith the Kasparov groups KK(A,B). This answers an open question posed by MarkHovey about the possibility of describing KK-theory for C*-algebras using thelanguage of Quillen model categories.

Realizing Kasparov's KK-theory groups as the homotopy classes of maps of a Quillen model category