If you want to use a custom <title>, there's a better and more elegant way to do this (although your request is rare the least).

Simple create a new extra field of type "text" that you will call "Page Title". Assign it to an existing or new extra fields group. Then make sure this group is assigned to your K2 categories (you can use a single K2 category as "category template" as well so you don't re-do the settings for each category again and again - see the "inherit" option inside the category form).

Then follow this guide getk2.org/documentation/tutorials/174-templating-with-k2-and-the-concepts-of-sub-templates to create your own set of K2 template overrides inside your Joomla template, so you can modify the output.

The point is this:
- Grab the value of the "Page Title" extra field directly: $this->item->extraFields->EXTRAFIELD_ALIAS_HERE->value (do this at the top of the item.php file)
- Reset the document title (right after "defined('_JEXEC') or die;") with:
Done.

FYI, customizations like this will come in the form of a new commercial offering for K2, pretty soon :)

Even simpler. Follow the process then to create a "Custom Title" extra field and replace:
With:(assuming you used "customtitle" as alias for that extra field)

Do the same in "category_item.php".

I urge to reconsider though this change as it requires lots of overrides in many more places as well (e.g. modules). Not to mention search results will not be very accurate if you use totally different custom titles from the actual given title in the K2 item form.