Bloody Cross

Bloody Cross is a manga about a half angel half vampire named Tsukimiya who is seeking a way to free herself from her half-blood curse, which will kill her if it isn't removed. While searching for a way to remove the curse, she is caught up in a "Holy War" among "God Candidates" who are competing against one another to gather "God's Inheritences", artifacts that contain God's power and can turn the candidate who gathers them into the new God.

Tropes used in Bloody Cross include:

Belligerent Sexual Tension: Tsukimiya and Hinata. Tsukimiya also has a little with Nao.
Bloody Murder: Tsukimiya can control her blood as a weapon.
Casting a Shadow: Momose. She can summon shadow beasts, use shadows for stealth, and use shadows in some kind of teleportation.
Catgirl: Momose is a cat demon, though her only feline feature is her tail.
Curse: Half-bloods all have cursed brands on their bodies that will kill them by the time they turn 18 unless they either drink the blood of a pure demon or find a God's inheritence with enough power to remove the curse.
Curse Escape Clause: See curse above.
Dhampyr: Tsukimiya and Hinata are both half vampire half angel.
Fake Defector: Hinata appears to be a traitor who joins Arcana, only for it to be revealed later that he was only pretending to change sides and was working for Tsuduki all along.
Fantastic Racism: Momose shows this toward half breeds, saying that they're "vulgar, barbaric and the lowest of the low".
Fallen Angel: Satsuki, one of the God Candidates.
Feather Motif: Satsuki. Whenever he shows up there's a rain of black feathers, even though he doesn't have wings.
Half-Human Hybrid: Nao is half human half angel.
Have You Seen My God?: God is apparently missing or no longer around and various people are competing to become his replacement.
Heel Face Revolving Door: Hinata can never seem to decide wether he's Tsukimiya's enemy or ally, seeming to want to help her one minute (and even getting past her lie detecting powers) then betraying her (once even shooting her several times) the next. Tsukimiya once commented that she was never sure which side of him she'd encounter. It's later revealed that he's a Fake Defector, and has always been on her side even when forced to fight her.
In the Back: Happens a few times.
Lecherous Licking: Momose licks Satsuki's fingers after returning to him from a mission.
Living Lie Detector: Tsukimiya.
The Mole: Nao has been working for Satsuki all along.
Once an Episode: Tsukimiya gets groped in almost every chapter.
Opera Gloves: Momose wears them in the first few chapters.
Our Angels Are Different: Tsuduki, a pure blood angel and God Candidate. He doesn't seem to have wings or a halo or any other angel features, and is generally childish and immature.
Paper Talisman: Most of Hinata's spells use them.
Pieces of God: God's Inheritences.
Stealth Hi Bye: Momose has done this a couple of times, thanks to her shadow manipulating powers allowing her to hide in people's shadows.
Thigh-High Boots: Momose, in the first few chapters. Tsukimiya has also worn this kind of boot once or twice.
Third Person Person: Momose.
Tomes of Prophecy and Fate: The Book of Prophecy and the Book of Da'at, two of the more recent and powerful God's Inheritences that appeared for the holy war.
Transferable Memory: Tsukimiya can read other people's memories by drinking their blood.
Voluntary Shapeshifting: Momose can make herself look like anyone. She usually uses it to make herself look like a friend of her enemy so she can get close enough to surprise attack the enemy.
Zettai Ryouiki: Tsukimiya. Momose as well in the first few chapters.