Leray-Hirsch theorem for K-theory

Statement
Let $$p:E \to B$$ be a fiber bundle with both $$E$$ and $$B$$ compact Hausdorff spaces and with fiber space $$F$$, such that :


 * $$K^*(F)$$ is free and finitely generated
 * There exist classes $$c_1, c_2, \ldots, c_k \in K^*(E)$$ that restrict to a freely generating set for $$K^*(F)$$ for each fiber $$F$$

And suppose one of these conditions holds:


 * 1) $$B$$ is a finite cell complex
 * 2) $$F$$ is a finite cell complex having only cells of even dimension

Then $$K^*(E)$$ is free as a module over $$K^*(B)$$, with basis $$\{ c_1, c_2, \ldots, c_k \}$$.