Eisenstein cohomology classes for GL N over imaginary quadratic fields

We study the arithmetic of degree N -1 Eisenstein cohomology classes for the locally symmetric spaces attached to GLN over an imaginary quadratic field k. Under natural conditions we evaluate these classes on (N -1)-cycles associated to degree N extensions L/k as linear combinations of generalized Dedekind sums. As a consequence we prove a remarkable conjecture of Sczech and Colmez expressing critical values of L-functions attached to Hecke characters of L as polynomials in Kronecker-Eisenstein series evaluated at torsion points on elliptic curves with complex multiplication by k. We recover in particular the algebraicity of these critical values.