The ca is a Lada 1200 (or VAZ 2101 "Zhiguli" in USSR). It's visually almost identical to the Italian Fiat 124, the Soviets bought the design and modified it to be more suitable for the rougher road conditions and weather.
Here's [1] a mish-mash of my favourite pictures from the rally, roughly in chronological order - from prep all the way to the finish. And here's the map of the route we did [2]. Nearly a year after finish, I still haven't finished writing up the whole trip though.