After years of controversy and substantial delays, the fissile materials storage facility at Mayak began accepting weapon-grade materials on July 11, 2006. It is not clear if this means that the United States and Russia eventually reached an agreement on the issues of transparency, access, and liability. This has been a contentious issue for quite a while and despite some signs of progress, no real progress has been reported (the "Securing the Bomb, 2006" report of the Managing the Atom project lists this issue as unresolved). Or maybe the United States had just given up on that and decided that secure storage of materials is more important. In any event, even if some kind of U.S. approval has been gained, the controversy in Russia is not quite over and Rosatom is trying to calm it by releasing some information about the facility.
According to Rosatom, the construction of the storage facility had been completed by December 2003. It has 3168 cells for containers, about half of which - 1689 - will be used for storing containers with fissile materials. The storage facility is operated by the FGUP PO Mayak (i.e. Rosatom) and guarded by the Interior Ministry (MVD) troops. The Directorate of the State Oversight of the Nuclear and Radiation Safety of the Ministry of Defense (UGNYaRB MO) provides an oversight of the facility.
Rosatom says that the construction has cost $397.5 million to the United States and "436,369.7 million rubles" to Russia, but I'm sure there is a mistake with the Russian number - at about 30 rubles per U.S. dollar it is close to $15 billion, which cannot possibly be true. Russia's contribution should be roughly on par with that of the United States. The exact number would probably be hard to tell, since the construction, which began in 1995, spanned through quite a few changes in the exchange rate.
The NTI web site has a good description of the project, but they stopped updating it in 2003.
UPDATE: Liablity issues are apparently covered by the CTR "umbrella agreement", which was extended in June 2006.