Classification of PL-structures on a homotopy type by K-theory

Consider the following question: given a finitely dominated CW complex $X$, how to describe the set of PL-structures on $X$? In fact, to obtain a good theory, one needs to modify the problem and consider the space of PL-structures on X up to s-cobordism. It turns out that the latter space has an algebraic description in terms of the Waldhausen K-theory of higher local system on $X$.
In my talk, I will construct a classifying space for PL-structures and formulate a theorem of Waldhausen, which describes it in terms of K-theory. Also I will give an explicit criterion when this space is non-empty and identify $\pi_1$ of this space with the Whitehead group of $\pi_1(X)$.