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The paper is a continuation of the works [17] of Vu and Shum, [18] and [19]of Vu and Hoa. In [17], Vu and Shum classified all the MD5-algebras havingcommutative derived ideals. In [18], Vu and Hoa considered foliations formed bythe maximal dimensional K-orbits (for short, MD5-foliations) of connectedMD5-groups such that their Lie algebras have 4-dimensional commutative derivedideals and gave a topological classification of the considered foliations. In[19], Vu and Hoa characterized the Connes' C*-algebras of some MD5-foliationsconsidered in \cite{VU-HO09} by the method of K-functors. In this paper, westudy K-theory for the leaf space of all MD5-foliations which are classified in[18] and characterize the Connes' C*-algebras of them by the method ofK-functors.

K-theory for the Leaf Space of Foliations Formed by the Generic K-orbits of a class of Solvable Real Lie Groups