The free loop space and the algebraic k-theory of spaces

Let A(X) be the space defined by Waldhausen whose homotopy groups define the algebraic K-groups of the space X and let $$B(X) = Q\sum (SE^1 {\text{ }} \times _{S^1 } \Lambda (X))$$ . Here ?(X) denotes the free loop space of X and Q denotes the functor O8S8. For X = SY, the suspension of a connected space Y, we shall prove that the homotopy fibers Ã(X), B(X) of the maps A(X) ? A (point), B(X) ? B (point) are equivalent as infinite loop spaces.