Currently, when a notification is shown for a task that is due, in order to complete it I have to unlock my phone, drag the notification area, click the notification, wait for the app to load (which can take several seconds), swipe the task, click it to complete, and click the Back button to go back to my home screen.

Not all of these steps can be avoided, but I'd the process to be as short as possible, as I complete a lot of tasks for which I have set due dates.

Specifically, I suggest allowing to complete the task instantly, without waiting for the whole app to load.
Perhaps there can be a lightweight process that can load just the specific task, while the main app loads in the background?