Is it permissible for the pilgrim in ihram to wear an umbrella hat that sits directly on the head?
Question

There is an umbrella that has an elastic band that goes around the head, but the head itself is bare. Is it permissible for the pilgrim in ihram to wear it?
Praise be to Allah.Firstly:
There is a clear prohibition on covering the head with something that sits directly on the head, and on wearing a turban.
It was narrated from ‘Abdullah ibn ‘Umar (may Allah be pleased with him) that a man said: O Messenger of Allah, what clothes may the pilgrim in ihram wear? The Messenger of Allah (blessings and peace of Allah be upon him) said: “He should not wear a chemise, a turban, trousers, a burnouse or khuffs.”  Narrated by al-Bukhari (1542) and Muslim (1177). The burnouse is a garment worn by the people of Morocco; it has an attached hood with which the head may be covered.
It was narrated from Ibn ‘Abbas (may Allah be pleased with him) that a man was thrown by his camel, broken his neck and died when we were with the Prophet (blessings and peace of Allah be upon him ihram) and he was in ihram. The Prophet (blessings and peace of Allah be upon him) said: “Wash him with water and lotus leaves, and shroud him in two pieces of cloth, but do not put any perfume on him or cover his head, for Allah will raise him on the Day of Resurrection reciting the Talbiyah.” Narrated by al-Bukhari (1267).
Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) said: “Do not cover his head” … This is general in meaning and applies to any kind of headcover."(Ash-Sharh al-Mumti‘  7/122).
With regard to the pilgrim in ihram covering his head, there are several categories:
-1- Covering it with something that sits directly on the head, such as a hat or turban and the like. This is prohibited. The evidence for it being prohibited is the hadith quoted above. 
-2- Covering his head with something that does not sit directly on it, such as an umbrella, tent, car roof etc. There is nothing wrong with this, because Umm Husayn (may Allah be pleased with her) said: I did Hajj with the Messenger of Allah (peace and blessings of Allah be upon him) during the Farewell Pilgrimage, and I saw him when he stoned Jamrat al-‘Aqabah and left on his mount, accompanied by Bilal and Usamah. One of them was leading his mount and the other was holding his garment over the head of the Messenger of Allah (peace and blessings of Allah be upon him), shading him from the sun. Narrated by Muslim (1298).
An-Nawawi (may Allah have mercy on him) said: 
This indicates that it is permissible for the pilgrim in ihram to shade his head with a cloth and the like. This is our view and the view of the majority of scholars, whether he is riding or walking."(Sharh an-Nawawi ‘ala Muslim  9/46).
Shaykh Ibn Baz (may Allah have mercy on him) said: There is nothing wrong with the pilgrim in ihram using an umbrella to protect himself from the sun, or seeking shade in a tent or under the roof of a car. "(Majmu‘ Fatawa Ibn Baz  17/115).
Shaykh Ibn `Uthaymin (may Allah have mercy on him) said: This is exactly like an umbrella."(Ash-Sharh al-Mumti‘  7/125).
He also said:
Shading oneself from the sun using an umbrella is not covering, because the one who is walking beside you can see all of your head. End quote.
-3-
Carrying something on one’s head. There is nothing wrong with this because it is usually not done with the intention of covering the head. If it is done with that intention, then it is prohibited. 
Shaykh Ibn Baz said: As for carrying something on one’s head, it does not come under the heading of covering the head that is prohibited, such as carrying food and the like, so long as he is not doing that as a trick (to get around the ruling), because Allah has forbidden His slaves to use trickery in order to do things that He has forbidden."(Majmu‘ Fatawa Ibn Baz  17/115).
Secondly:
What appears to be the case is that the umbrella that has elastic that goes all around the head comes under the ruling on turbans and is subject to the prohibition mentioned in the texts, because the elastic goes all around the head, as a turban does, and covers part of the head.
It says in al-Mawsu‘ah al-Fiqhiyyah al-Kuwaitiyyah (2/154):
It is also haram to cover part of the head with something that is regarded as covering or is intended for the purpose of covering… So it is not permissible for him to tie a bandana or band around his head, or to put on his head anything that sits directly on it and stays there. End quote.
The elastic which holds the umbrella hat in place is like a band and more so, as is well known and is widely seen.
The Permanent Committee for Ifta’ was asked:
This is a sample for you to see of a small umbrella that offers protection from the sun, and is tied to the head. The manufacturers of this small umbrella want to know whether it is allowed to use it during Hajj so that they can distribute it, either as gifts or as an item that is sold. Therefore I hope that you can tell me your opinion regarding that, so that we may proceed.
They replied: This band with which the umbrella that protects against the sun is tied to the head comes under the same ruling as turbans. It is not permissible for the pilgrim in ihram to wear it, because the Prophet (blessings and peace of Allah be upon him) said: “The pilgrim in ihraam should not wear a chemise, or a turban, or trousers, or a burnouse.” The authenticity of the hadith is agreed upon."(Fatawa al-Lajnah ad-Da’imah vol. 2, 10/141).
Based on that:
It is not permissible for men in ihram to wear the umbrella hat that is tied to the head. They can do without that by using the type of umbrella that is carried in the hand.
And Allah knows best.