Universal coefficient formulas for stable $K$-theory

The goal of this paper is to establish a Künneth spectral sequence and the connections between the stable complex $K$-functor $k^*$ and other generalized cohomology theories for some classes of cell complexes (Theorems 1 and 3). In Theorem 2 criteria are formulated for a finite cell complex to admit a $k^*$-resolution. Analogous results were also obtained by Landweber [3].