---
abstract: 'We introduce a class of orders on ${\mathbb{P}}^d$ called Geigle-Lenzing orders and show that they have tilting bundles. Moreover we show that their module categories are equivalent to the categories of coherent sheaves on Geigle-Lenzing projective spaces introduced in [@HIMO].'
address:
- 'O. Iyama: Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602 Japan'
- 'B. Lerner: Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602 Japan'
author:
- Osamu Iyama
- Boris Lerner
title: 'Tilting bundles on orders on ${\mathbb{P}}^d$'
---

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Introduction
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Throughout we work over a field $k$. Moreover, for an order $\Lambda$ we denote by ${\operatorname{\mathsf{mod}}}\Lambda$ the category of coherent left $\Lambda$-modules.

Weighted projective lines were first introduced by Geigle and Lenzing [@GL] and play an important role in representation theory (e.g. [@Me; @CK; @KLM]) and homological mirror symmetry (e.g. [@KST; @U]). It has been pointed out in both [@CI] and [@RVdB] that the category of coherent sheaves on a weighted projective line is equivalent to the module category of a hereditary order on ${\mathbb{P}}^1$, where by an *order* we mean a certain coherent sheaf of non commutative algebras. However, until now, this has remained only an observation and has not been 