integrate Gmail API in web application

We want to accomplish the following in our web application: 1. Integrate user's Gmail account through authentication 2. Retrieve user's Gmail mailbox (once the user approves) in the mail interface of the web application 3. If the user sends any email from the web application's interface that mail should be available in the Sent folder of the user's Gmail account. 4. Even if the user sends any email from his gmail account in the normal way, that mail and its responses should be available in the web application Basically, the web application will act as his new mail interface powered by Gmail. Having said so, the web application is a CRM and we can integrate this module in it. So, you will have to give us the module which we will integrate in our application. You can create a demo mailing interface and give us the code and the rest we will do. Our platform is on Laravel so if you develop it for Laravel, it will be good for us. However, if we get it in core PHP, we can integrate in our environment. Additional requirement: We need a Chrome browser extension for this so that as the user opens his Gmail on Chrome, the extension should open the web application's interface as well.