Service Worker at Google Chrome Extension. I really want to, but it hurts?

Question

JavaScript

Previously asked the question Why does caching not work?
The question concerns exactly the chrome extention.
I fetch templaters and they are not cached.
Then I remembered about sw and its power in appCatch.
He took his hands and pressed the buttons, it turned out.

if ('serviceWorker' in navigator) {
    window.addEventListener('load', function() {
        navigator.serviceWorker.register('/js/sw.js').then(function(registration) {
            console.log('ServiceWorker registration successful with scope: ', registration.scope);
        }).catch(function(err) {
            console.log('ServiceWorker registration failed: ', err);
        });
    });
}

sw.js

var CACHE_NAME = 'my-site-cache-v1';
var urlsToCache = [
  '/html/templater/popUpId.tpl',
  '/html/templater/bodyId.tpl',
  '/html/templater/topNavLog.tpl',
  '/html/templater/topNav.tpl',
  '/html/templater/bodyFailedAuth.tpl',
  '/html/templater/registration.tpl',
  '/html/templater/login.tpl',
  '/html/templater/syncToServ.tpl',
  '/html/templater/syncToPc.tpl',
  '/html/templater/emptySearch.tpl',
  '/html/templater/updateButton.tpl',
  '/html/templater/notification.tpl'
];
self.addEventListener('install', function(event) {
  event.waitUntil(
    caches.open(CACHE_NAME)
      .then(function(cache) {
        return cache.addAll(urlsToCache);
      })
  );
});

Ran.
Look in console and there sis.
ServiceWorker registration successful with scope
And then

Uncaught (in promise) TypeError: Add/AddAll does not support schemes other than "http" or "https"

Is it possible to somehow use sw in the Orthodox chrome-extension:// and not in this http of yours?
Are there any workarounds that anyone has come across? Fetschit not from local but from remote? Not a good idea as I'm claiming the "Offline Application" achievement.