In the former Soviet Union, what did the head of state do?

I am specifically talking about Mikhail Kalinin. In most European countries, the head of state oversees foreign and diplomatic issues, including negotiations and the signing of treaties. In the USSR, however, the head of government (Premier) did all of the domestic and foreign work (e.g. Molotov signed the 1939 nonaggression pact with Germany; Stalin, as Premier, attended the Tehran, Yalta, and Potsdam conferences). Other than sitting at a desk telling people they are "President" or "head of state", what exactly did Kalinin and his successors do?