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This is an updated and expanded version of my preprint #68 in the K-theory server at Urbana (which was an abstract of my talk at Vechta conference on commutative algebra, 1994). In §2 two conjectures on nilpontency of the 'monoid Frobenius action' on the K-theory of toric cones and on stabilizations of the corresponding K-groups are stated. Both of these conjectures are higher analogues of Anderson's conjecture and their proof would bring a rather complete understanding of Ktheory of toricdoi:10.4310/hha.1999.v1.n1.a5 fatcat:lboceynmevdzdmc4q232lp2the