(joint with Johannes Sprang). Let K be a CM ?eld and L/K be an extension of degree n and ? be an algebraic critical Hecke character of L. Then we show that the L-value L(?, 0) divided by a carefully normalized Shimura-Katz period is integral and construct in the ordinary case a p-adic L-function for ?. This generalizes results by Damerell, Shimura and Katz for CM ?elds (L = K) and settles all remaining open cases of algebraicity of critical Hecke L-values. Our method relies on the construction of new equivariant Eisenstein-Kronecker cohomology classes using the completion of the Poincar´e bun-dle. Here we were inspired by work of Bannai-Kobayshi in the imaginary quadratic case. Our method is even in the classical CM case completely dif-ferent from the approaches by Shimura and Katz. With a technique, which was pioneered in Sprang?s thesis, this approach leads without any computa-tions directly to the construction of measures giving the p-adic L-functions for ?. For ZOOM Meeting-ID + Passcode write to: ebodon@uni-muenster.de