spoilers Avatar fits perfectly into the Cosmere, in this essay I will--

[Nicosium Skaa]

Disclaimer: I have no idea where to put this, so please benevolent mods, move this if necessary.

SPOILER WARNING: Alright so, this theory contains the heaviest spoilers in the world for Stormlight Archive Rhythm of War, Warbreaker, Elantris, Tress of the Emerald Sea, and I might have to borrow from Mistborn Era 2
It also spoilers ALL of Avatar the last airbender and Legend of Korra.

 

The world of Avatar almost perfectly fits into the cosmere, here me out.
I'll be using cosmere words like Bond, Connection, Investiture, Spren, Shards, cognitive realm, Intent, and the like, so if you don't know any of those, read the cosmere books before reading on in this theory. I'll to capitalize those words in order to make them stand out.

I will call the Avatar-World the Avatar-World in order to avoid confusion.

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Let's get started, first of all, of course there are not really fitting shards left over for this planet, but to put it simply, something similar to Roshar is going on.
Spren-like splinters called Spirits inhabit the Cognitive Realm known as the Spirit-world of the planet Avatar-World, and two perpendicularities known as Spirit Portals in the North and South pole of the planet exist. This is a fact that points towards two Shards of Adonalsium having been shattered on that world.

The Spirit World, Spirits, and the Perpendicularities
Judging from the original humans having been in the Cognitive Realm first, they might've migrated over from another planet, before having been changed by Cosmereological Intent (see Pure Lakers on Roshar) to let the ever present but Mist-like (see Scadrial) invisible form of Investiture known as Chi, flow through their bodies.
The Spren/spirits/splinters of those Shards known as the lion turtles could thus grant the humans a special form of Bond to allow them to use the power of an element.

In the Avatar-World there must be two new types of Bonds: one that lion turtles use to grant the ability to use investiture to control and element, and one bond that Spirits use to possess a human.

Bending and Investiture - an End-Positive System
Forming a Connection to the power of the Splintered shards (see what happened on Sel), this Bond is not very similar to the Nahel Bond (Roshar & Spren) and a Luhel Bond (Lumar), but instead only requires an initial bond that unlcoks the power in a human and can then be passed on genetically.
Investiture in the Avater-World in the physical realm is an invisible gas, or at least humans have evolved to not see it, and is ever-present, seeping into the humans where it is called Chi.
The unlocking of bending and chi-gates might form cracks in the soul that are passed on genetically, seemingly even the more powerful Splinters or rather Cognitive Shadows can hold such powers, as evident by Raava and Vaatu.

Bending itself is a way of Accessing Investiture, requiring intent and specific physical movements that look almost like a martial art. This is similar to Aons drawn by Elantrians using AonDor or the martial arts on Sel.

The Avatar
Both bonds were used by Raava and Wan to create the first avatar: A cognitive shadow that holds memories of all prior avatars, held together within a human body by the Spirit Raava.
Whenever an Avatar dies, the memories are added to the cognitive shadow known as the Avatar, and the spirit Raava carries it on to a newborn human from another nation to use the possession Bond with.
Similar to a Bondsmith, the Avatar can create and sever connection, such as completely taking someone's ability to bend, or temporarily elsecalling into the Spirit World (Cognitive Realm).

Chi-Blocking 
Chi-blocking blocks spiritual pathways for the Soul which investiture would need to take.

Healing
Healing works well in the Avatar-World since due to the physical movements through which investiture is accessed, the humans of the Avatar-World have developed a stronger image of self and their cultures, even associating them directly with how they can use investiture.

Savantism
Savantism in bending might require something more than just a lot of investiture and using their power, but these are known as specialized bending types.

 

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Tell me what you think. Did I make any mistakes? Any way you can fix my mistakes and still make it fit?