The Mediator (1990)

In an ordinary industrial Soviet town, notable only for presence of a radio-telescope, people start behaving strangely, in a robotic manner, while assuming geometry-inspired aliases and organizing into a new hierarchy. The phenomenon spreads via a device of alien origin, called "the intermediary" ("posrednik"), capable of implanting extraterrestrial minds into human bodies. The aliens are bound by limitations of the terrestrial technology, having to use the means at the disposal of humans to prepare the grounds for the full-scale invasion. With "the intermediary" being unable to subdue minds of children, lunatics, geniuses, and rebels, a struggle over the fate of the town and the human civilization ensues.