  We construct a motivic spectral sequence for the relative homotopy invariant
K-theory of a closed immersion of schemes $D \subset X$. The $E_2$-terms of
this spectral sequence are the cdh-hypercohomology of a complex of
equi-dimensional cycles.
  Using this spectral sequence, we obtain a cycle class map from the relative
motivic cohomology group of 0-cycles to the relative homotopy invariant
K-theory. For a smooth scheme $X$ and a divisor $D \subset X$, we construct a
canonical homomorphism from the Chow groups with modulus $\CH^i(X|D)$ to the
relative motivic cohomology groups $H^{2i}(X|D, \Z(i))$ appearing in the above
spectral sequence. This map is shown to be an isomorphism when $X$ is affine
and $i = \dim(X)$.
