Collins Russian Dictionary 2nd Edition © HarperCollins Publishers 2000, 1997:
foster [ˈfɔstər] vt (child) брать*(взять*perf) на воспита́ние (activity) поощря́ть (impf) (hope) пита́ть (impf)
to foster an idea вына́шивать (impf) мысль
* is used to mark translations which have irregular inflections. The Russian-English side of the dictionary gives inflectional information.