Authenticate MVC client against self-hosted Web API (OWIN/Katana)

I have a Windows Service running a Web API hosted as a OWIN middleware - the server. The API uses application cookie authentication and validates users against a database, using OWINs identity model. Now I would like to authenticate a user who accesses the API through a standard MVC web application (the client), but I'm unsure how to achieve this, e.g. after I received a response along with the cookie from the API, where do I have to store it inside the MVC application so that the cookie will be automatically sent along with further API calls.