An adjective or noun for someone who "has a lot of gall"?

What would be a suitable term for someone who has a lot of gall or has the gall to? Specifically someone who has wronged you or yours, or taken something from you, and should be repentant (and perhaps, absent), but shows up and shows no remorse or shame. I’m thinking of something more specific than shameless (because that can have such varied applications, terms like like shameless self-promotion wouldn’t really apply).

A better example might be someone who has borrowed from you repeatedly, even stolen some money from you — and then comes back asking for a loan, with a smile. Is there a spot-on adjective for that person? Or a noun? (“He’s a ____; he asked me for another $100!”).

Solution 1:

I would say such a person was brazen

ˈbreɪz(ə)n
adjective
1. bold and without shame.

(oxforddictionaries.com)

For the example given:

He’s brazen; he asked me for another $100!

or more effectively:

He’s a brazen [expletive]; he asked me for another $100!

Solution 2:

I would call this person audacious (adjective) or say that he/she has chutzpah (noun). The word "audacious" can be in a positive or negative fashion, so the speaker can use tone of voice to determine which one is meant. This sort of subtlety lends a certain intimacy to conversations.

According to the Cambridge dictionary, audacious means:

audacious adjective UK /ɔːˈdeɪ.ʃəs/ US /ɑː-/

showing a willingness to take risks or offend people: He described the plan as ambitious and audacious. an audacious remark/suggestion

and chutzpah means:

chutzpah noun chutz·pah \ˈhu̇t-spə, ˈḵu̇t-, -(ˌ)spä\

: personal confidence or courage that allows someone to do or say things that may seem shocking to others

Solution 3:

You could say that they have brass neck

A type of behaviour where someone is extremely confident about their own actions but does not understand that their behaviour is unacceptable to others.

_{Cambridge Dictionary}

In your example: He's got a brass neck; he asked me for $100!

Alternatively, you could use the synonymous term effrontery.

Extreme rudeness without any ability to understand that your behaviour is not acceptable to other people

_{Cambridge Dictionary}

After having stolen from me, he had the effrontery to ask for $100!

Solution 4:

Perhaps the person is acting entitled. More commonly, for the pejorative sense, the noun form, entitlement is used

The belief that one is inherently deserving of privileges or special treatment: no wonder your kids have a sense of entitlement

[AS MODIFIER]: this entitlement mentality is completely out of control

Oxford Dictionaries Online

Also, the term balls is sometimes used to convey arrogant action

(uncountable, slang) Bravery, courage, chutzpah, or brazenness.  

He must have a lot of balls to talk to his boss that way.

He's the guy with the big balls in that group.

Balls is all that it takes to succeed.

Wiktionary

Note that the term is often used admiringly, and the negative connotation is more tonal or contextual than literal. In the example given by the OP, you might say

You've got a lot of balls to ask for more money when you already owe me $100!

Also note that this usage is very much slang, is somewhat sexist, and would be considered rude and objected to by many.