This is an announcement for the paper "Linearly ordered compacta and Banach spaces with a projectional resolution of the identity" by Wieslaw Kubis. Abstract: We construct a compact linearly ordered space $K$ of weight aleph one, such that the space $C(K)$ is not isomorphic to a Banach space with a projectional resolution of the identity, while on the other hand, $K$ is a continuous image of a Valdivia compact and every separable subspace of $C(K)$ is contained in a 1-complemented separable subspace. This answers two questions due to O. Kalenda and V. Montesinos. Archive classification: Functional Analysis; General Topology Mathematics Subject Classification: Primary: 46B03, 46B26; Secondary: 54F05, 46E15, 54C35 Remarks: 13 pages The source file(s), cmplmntn_property6.tex: 45742 bytes, is(are) stored in gzipped form as 0602628.gz with size 14kb. The corresponding postcript file has gzipped size 66kb. Submitted from: wkubis@pu.kielce.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0602628 or http://arXiv.org/abs/math.FA/0602628 or by email in unzipped form by transmitting an empty message with subject line uget 0602628 or in gzipped form by using subject line get 0602628 to: math@arXiv.org.