Is it possible to execute a function on a user object in Twig?

Question

You can use hook_entity_load to add fields to the user object like so:

function mymodule_entity_load($entities, $type)
{
    if ($type == 'user'  )
    {
       foreach($entities as $e) {
         $e->myField = 'hello';
       }
    }
}

That will allow me to do this in twig:

{{ user.myField }}

This is quite useful, but it would be great if I could do this:

{{ user.getActivity() }}

Or more specifically:

<h1>Members</h1>
<ul>
    {% for activity in user.getActivity()  %}
        <li>{{ activity.time }}</li>
    {% endfor %}
</ul>

Is there a way to add a "function" in this way?