A twisted class number formula and Gross's special units over an imaginary quadratic field

Let F/k be a finite abelian extension of number fields with k imaginary quadratic. Let O-F be the ring of integers of F and n >= 2 a rational integer. We construct a submodule in the higher odd-degree algebraic K-groups of OF using corresponding Gross's special elements. We show that this submodule is of finite index and prove that this index can be computed using the higher "twisted" class number of F, which is the cardinal of the finite algebraic K-group K2n-2(O-F).