This is an announcement for the paper "A generalization of the Markov-Kakutani fixed point theorem" by Jaroslaw Wawrzycki. Abstract: In this announcement we generalize the Markov-Kakutani fixed point theorem for abelian semi-groups of affine transformations extending it on some class of non-commutative semi-groups. As an interesting example we apply it obtaining a generalization of the invariant version of the Hahn-Banach theorem. Archive classification: Functional Analysis Mathematics Subject Classification: 46A22, 46A55 Remarks: 5 pages, Latex preparation The source file(s), kakutani.tex: 11176 bytes, is(are) stored in gzipped form as 0402255.gz with size 4kb. The corresponding postcript file has gzipped size 32kb. Submitted from: Jaroslaw.Wawrzycki@ifj.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0402255 or http://arXiv.org/abs/math.FA/0402255 or by email in unzipped form by transmitting an empty message with subject line uget 0402255 or in gzipped form by using subject line get 0402255 to: math@arXiv.org.