how to redirect to external url from c# controller

Use the Controller’s Redirect() method.

public ActionResult YourAction()
{
    // ...
    return Redirect("http://www.example.com");
}

Update

You can’t directly perform a server side redirect from an ajax response. You could, however, return a JsonResult with the new url and perform the redirect with javascript.

public ActionResult YourAction()
{
    // ...
    return Json(new {url = "http://www.example.com"});
}

$.post("@Url.Action("YourAction")", function(data) {
    window.location = data.url;
});